Journal articles: 'Solitary waves'

1

Fitzgerald, Richard J. "Interacting solitary waves." Physics Today 65, no. 11 (November 2012): 20. http://dx.doi.org/10.1063/pt.3.1777.

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2

Weidman, P. D., and R. Zakhem. "Cylindrical solitary waves." Journal of Fluid Mechanics 191, no. -1 (June 1988): 557. http://dx.doi.org/10.1017/s0022112088001703.

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3

Mason, Joanne, and Edgar Knobloch. "Solitary dynamo waves." Physics Letters A 355, no. 2 (June 2006): 110–17. http://dx.doi.org/10.1016/j.physleta.2006.02.013.

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4

Qureshi, M. N. S., Jian Kui Shi, and H. A. Shah. "Electrostatic Solitary Waves." Journal of Fusion Energy 31, no. 2 (June 14, 2011): 112–17. http://dx.doi.org/10.1007/s10894-011-9439-7.

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5

Weidman, P. D., and M. G. Velarde. "Internal Solitary Waves." Studies in Applied Mathematics 86, no. 2 (February 1992): 167–84. http://dx.doi.org/10.1002/sapm1992862167.

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6

Chen, X. N., and W. Maschek. "Nuclear solitary waves." PAMM 8, no. 1 (December 2008): 10489–90. http://dx.doi.org/10.1002/pamm.200810489.

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7

Lubin, Pierre, and Stéphane Glockner. "NUMERICAL SIMULATIONS OF BREAKING SOLITARY WAVES." Coastal Engineering Proceedings 1, no. 33 (September 28, 2012): 59. http://dx.doi.org/10.9753/icce.v33.waves.59.

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This paper presents the application of a parallel numerical code to breaking solitary waves impacting a seawall structure. The three-dimensional Navier-Stokes equations are solved in air and water, coupled with a subgrid-scale model to take turbulence into account. We compared three numerical methods for the free-surface description, using the classical VOF-PLIC and VOF-TVD methods, and an original VOF-SM method recently developed in our numerical tool (Vincent et al., 2010). Some experimental data for solitary waves impinging and overtopping coastal structures are available in literature (Hsiao et al., 2010). Solitary waves are often used to model tsunami behaviors because of their hydrodynamic similarities. From a numerical point of view, it allows shorter CPU time simulations, as only one wave breaks. Here we apply the model to simulate three-dimensional solitary waves and compare qualitatively our results with the experimental data. We investigate three configurations of solitary waves impinging and overtopping an impermeable seawall on a 1:20 sloping beach.

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Cai, Huixian, Chaohong Pan, and Zhengrong Liu. "Some Interesting Bifurcations of Nonlinear Waves for the Generalized Drinfel’d-Sokolov System." Abstract and Applied Analysis 2014 (2014): 1–20. http://dx.doi.org/10.1155/2014/189486.

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We study the bifurcations of nonlinear waves for the generalized Drinfel’d-Sokolov systemut+(vm)x=0,vt+a(vn)xxx+buxv+cuvx=0calledD(m,n)system. We reveal some interesting bifurcation phenomena as follows. (1) ForD(2,1)system, the fractional solitary waves can be bifurcated from the trigonometric periodic waves and the elliptic periodic waves, and the kink waves can be bifurcated from the solitary waves and the singular waves. (2) ForD(1,2)system, the compactons can be bifurcated from the solitary waves, and the peakons can be bifurcated from the solitary waves and the singular cusp waves. (3) ForD(2,2)system, the solitary waves can be bifurcated from the smooth periodic waves and the singular periodic waves.

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9

LAMB, KEVIN G. "A numerical investigation of solitary internal waves with trapped cores formed via shoaling." Journal of Fluid Mechanics 451 (January 25, 2002): 109–44. http://dx.doi.org/10.1017/s002211200100636x.

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The formation of solitary internal waves with trapped cores via shoaling is investigated numerically. For density fields for which the buoyancy frequency increases monotonically towards the surface, sufficiently large solitary waves break as they shoal and form solitary-like waves with trapped fluid cores. Properties of large-amplitude waves are shown to be sensitive to the near-surface stratification. For the monotonic stratifications considered, waves with open streamlines are limited in amplitude by the breaking limit (maximum horizontal velocity equals wave propagation speed). When an exponential density stratification is modified to include a thin surface mixed layer, wave amplitudes are limited by the conjugate flow limit, in which case waves become long and horizontally uniform in the centre. The maximum horizontal velocity in the limiting wave is much less than the wave's propagation speed and as a consequence, waves with trapped cores are not formed in the presence of the surface mixed layer.

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10

Kenyon, Kern E. "Stability of Solitary Waves." Physics Essays 14, no. 3 (September 2001): 266–69. http://dx.doi.org/10.4006/1.3025492.

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11

Chen, Yijiang, and Javid Atai. "Parametric spatial solitary waves." Optics Letters 19, no. 17 (September 1, 1994): 1287. http://dx.doi.org/10.1364/ol.19.001287.

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12

Craig, Walter, and Peter Sternberg. "Symmetry of solitary waves." Communications in Partial Differential Equations 13, no. 5 (January 1988): 603–33. http://dx.doi.org/10.1080/03605308808820554.

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13

Stoychev, K. T., M. T. Primatarowa, and K. Marinov. "Exciton-polariton solitary waves." European Physical Journal B - Condensed Matter 29, no. 2 (September 1, 2002): 301–4. http://dx.doi.org/10.1140/epjb/e2002-00305-8.

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14

Părău, Emilian I. "Solitary interfacial hydroelastic waves." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2111 (December 11, 2017): 20170099. http://dx.doi.org/10.1098/rsta.2017.0099.

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Solitary waves travelling along an elastic plate present between two fluids with different densities are computed in this paper. Different two-dimensional configurations are considered: the upper fluid can be of infinite extent, bounded by a rigid wall or under a second elastic plate. The dispersion relation is obtained for each case and numerical codes based on integro-differential formulations for the full nonlinear problem are derived. This article is part of the theme issue ‘Nonlinear water waves’.

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15

Puerta, J., and P. Martin. "Bi-dust solitary waves." Journal of Physics: Conference Series 370 (June 19, 2012): 012042. http://dx.doi.org/10.1088/1742-6596/370/1/012042.

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16

Vanden-Broeck, J. M., and Joseph B. Keller. "Surfing on solitary waves." Journal of Fluid Mechanics 198, no. -1 (January 1989): 115. http://dx.doi.org/10.1017/s0022112089000066.

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17

Poladian, L., A. W. Snyder, and D. J. Mitchell. "Low-interaction solitary waves." Optics Communications 91, no. 1-2 (July 1992): 97–98. http://dx.doi.org/10.1016/0030-4018(92)90108-4.

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18

Guoxiang, Huang, Lou Senyue, and Dai Xianxi. "Cylindrical envelope solitary waves." Chinese Physics Letters 7, no. 9 (September 1990): 398–401. http://dx.doi.org/10.1088/0256-307x/7/9/005.

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19

Lanzano, Paolo. "Solitary waves of vortices." Earth, Moon, and Planets 69, no. 3 (1995): 271–83. http://dx.doi.org/10.1007/bf00643788.

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20

Sutherland, B. R., K. J. Barrett, and G. N. Ivey. "Shoaling internal solitary waves." Journal of Geophysical Research: Oceans 118, no. 9 (September 2013): 4111–24. http://dx.doi.org/10.1002/jgrc.20291.

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21

Baldock, T. E., D. Peiris, and A. J. Hogg. "Overtopping of solitary waves and solitary bores on a plane beach." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2147 (July 18, 2012): 3494–516. http://dx.doi.org/10.1098/rspa.2011.0729.

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The overtopping of solitary waves and bores present major hazards during the initial phase of tsunami inundation and storm surges. This paper presents new laboratory data on overtopping events by both solitary waves and solitary bores. Existing empirical overtopping scaling laws are found to be deficient for these wave forms. Two distinct scaling regimes are instead identified. For solitary waves, the overtopping rates scale linearly with the deficit in run-up freeboard. The volume flux in the incident solitary wave is also an important parameter, and a weak dependence on the nonlinearity of the waves ( H / d ) is observed. For solitary bores, the overtopping cannot be scaled uniquely, because the fluid momentum behind the incident bore front is independent of the bore height, but it is in close agreement with recent solutions of the nonlinear shallow water equations. The maximum overtopping rate for the solitary waves is shown to be the lower bound of the overtopping rate for the solitary bores with the same deficit in freeboard. Thus, for a given run-up, the solitary bores induce greater overtopping rates than the solitary waves when the relative freeboard is small.

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22

BAKHOLDIN, I., A. IL'ICHEV, and A. ZHARKOV. "Steady magnetoacoustic waves and decay of solitonic structures in a finite-beta plasma." Journal of Plasma Physics 67, no. 1 (January 2002): 1–26. http://dx.doi.org/10.1017/s0022377801001337.

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The solitonic, periodic and quasiperiodic solutions that obey the full system of transport equations describing one-dimensional motion of a isotropic collisionless quasineutral plasma in a magnetic field are treated. The domains of physical parameters of such a plasma are determined for fast and slow magnetoacoustic branches, where solitary waves and generalized solitary waves exist. In the parameter domain where solitary waves are replaced by non-local generalized solitary waves, the localized disturbances are subject to decay, which has qualitatively different mechanisms for fast and slow magnetoacoustic waves. The specific feature of the decay process for fast waves is found to be characterized by a decrease of energy of the disturbance due to quasistationary radiation of a resonant periodic wave of the same nature. Analogous disturbances, having the form of a slow magnetoacoustic solitary wave core, practically do not radiate resonant Alfvénic modes, but rapidly lose energy as a result of continuous shedding of a slow-wave component. Various types of shock waves are also considered. Their structure is formed by existing solitonic configurations – solitary and generalized solitary waves. Possibilities of observations of solitary waves and their decay in a real plasma are discussed.

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23

Su, Chau-Hsing, and Qi-su Zou. "Waves generated by collisions of solitary waves." Physical Review A 35, no. 11 (June 1, 1987): 4738–42. http://dx.doi.org/10.1103/physreva.35.4738.

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24

Xu, Chengzhu, and Marek Stastna. "On the interaction of short linear internal waves with internal solitary waves." Nonlinear Processes in Geophysics 25, no. 1 (January 17, 2018): 1–17. http://dx.doi.org/10.5194/npg-25-1-2018.

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Abstract. We study the interaction of small-scale internal wave packets with a large-scale internal solitary wave using high-resolution direct numerical simulations in two dimensions. A key finding is that for wave packets whose constituent waves are short in comparison to the solitary wave width, the interaction leads to an almost complete destruction of the short waves. For mode-1 short waves in the packet, as the wavelength increases, a cutoff is reached, and for larger wavelengths the waves in the packet are able to maintain their structure after the interaction. This cutoff corresponds to the wavelength at which the phase speed of the short waves upstream of the solitary wave exceeds the maximum current induced by the solitary wave. For mode-2 waves in the packet, however, no corresponding cutoff is found. Analysis based on linear theory suggests that the destruction of short waves occurs primarily due to the velocity shear induced by the solitary wave, which alters the vertical structure of the waves so that significant wave activity is found only above (below) the deformed pycnocline for overtaking (head-on) collisions. The deformation of vertical structure is more significant for waves with a smaller wavelength. Consequently, it is more difficult for these waves to adjust to the new solitary-wave-induced background environment. These results suggest that through the interaction with relatively smaller length scale waves, internal solitary waves can provide a means to decrease the power observed in the short-wave band in the coastal ocean.

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25

Il'ichev, A. T. "Solitary and generalized solitary waves in dispersive media." Journal of Applied Mathematics and Mechanics 61, no. 4 (January 1997): 587–600. http://dx.doi.org/10.1016/s0021-8928(97)00076-2.

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26

Yu, Wen, Fenggang Wang, Jianguo Lin, and Dong Li. "Numerical Simulation of the Force Acting on the Riser by Two Internal Solitary Waves." Applied Sciences 12, no. 10 (May 11, 2022): 4873. http://dx.doi.org/10.3390/app12104873.

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An internal wave is a typical dynamic process. As an internal wave, an internal solitary wave usually occurs between two layers of fluids with different densities. Compared with general internal waves, internal solitary waves have large amplitudes, fast propagation speeds, short-wave periods, and often have tremendous energy. The propagation causes strong convergence and divergence of seawater and generates a sudden strong current. Due to its various characteristics, the propagation of internal solitary waves can cause serious harm to offshore engineering structures. Therefore, studying the effects of internal solitary waves on risers is vital in preventing environmental pollution caused by riser damage. Although the research on internal solitary waves has achieved very fruitful results, the research on structures is mostly focused on a single condition, and the occurrence of internal solitary wave, as a complex ocean phenomenon, is often accompanied by many situations. Therefore, this paper constructs a numerical simulation of the interaction between two columns of internal solitary waves and risers. This study explores the force and flow field changes of the riser under the condition of multiple internal solitary waves using the Star-CCM+ software in the simulation. The improved K-epsilon turbulence model was adopted to close the three-dimensional incompressible Navier–Stokes equation, and the solitary wave solution of the eKdV equation was used as the initial and boundary conditions. The interaction between single and double internal solitary waves and a riser was calculated, compared, and analyzed using numerical analysis. The experiment results indicate that the conditions of two internal solitary waves differ from those of a single internal solitary wave. After colliding at the riser, the waves gradually merge into a single wave, and the flow field reaches its minimum velocity. Under the two-wave condition, the horizontal force on the riser as a whole is less than the single-wave condition. As the amplitude difference between the two internal solitary waves gradually decreases, the horizontal opposing force received by the riser first increases and then decreases, while the horizontal positive force gradually decreases.

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27

Nakayama, Keisuke, Taro Kakinuma, Hidekazu Tsuji, and Masayuki Oikawa. "NONLINEAR OBLIQUE INTERACTION OF LARGE AMPLITUDE INTERNAL SOLITARY WAVES." Coastal Engineering Proceedings 1, no. 33 (October 9, 2012): 19. http://dx.doi.org/10.9753/icce.v33.waves.19.

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Solitary waves are typical nonlinear long waves in the ocean. The two-dimensional interaction of solitary waves has been shown to be essentially different from the one-dimensional case and can be related to generation of large amplitude waves (including ‘freak waves’). Concerning surface-water waves, Miles (1977) theoretically analyzed interaction of three solitary waves, which is called “resonant interaction” because of the relation among parameters of each wave. Weakly-nonlinear numerical study (Funakoshi, 1980) and fully-nonlinear one (Tanaka, 1993) both clarified the formation of large amplitude wave due to the interaction (“stem” wave) at the wall and its dependency of incident angle. For the case of internal waves, analyses using weakly nonlinear model equation (ex. Tsuji and Oikawa, 2006) suggest also qualitatively similar result. Therefore, the aim of this study is to investigate the strongly nonlinear interaction of internal solitary waves; especially whether the resonant behavior is found or not. As a result, it is found that the amplified internal wave amplitude becomes about three times as much as the original amplitude. In contrast, a "stem" was not found to occur when the incident wave angle was more than the critical angle, which has been demonstrated in the previous studies.

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28

Kapitula, Todd. "Bifurcating bright and dark solitary waves for the perturbed cubic-quintic nonlinear Schrödinger equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 3 (1998): 585–629. http://dx.doi.org/10.1017/s030821050002165x.

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The existence of bright and dark multi-bump solitary waves for Ginzburg–Landau type perturbations of the cubic-quintic Schrodinger equation is considered. The waves in question are not perturbations of known analytic solitary waves, but instead arise as a bifurcation from a heteroclinic cycle in a three-dimensional ODE phase space. Using geometric singular perturbation techniques, regions in parameter space for which 1-bump bright and dark solitary waves will bifurcate are identified. The existence of N-bump dark solitary waves (N ≧ 1) is shown via an application of the Exchange Lemma with Exponentially Small Error. N-bump bright solitary waves are shown to exist as a consequence of the work of Kapitula and Maier-Paape.

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29

Kozlov, Vladimir, Evgeniy Lokharu, and Miles H. Wheeler. "Nonexistence of Subcritical Solitary Waves." Archive for Rational Mechanics and Analysis 241, no. 1 (May 17, 2021): 535–52. http://dx.doi.org/10.1007/s00205-021-01659-y.

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AbstractWe prove the nonexistence of two-dimensional solitary gravity water waves with subcritical wave speeds and an arbitrary distribution of vorticity. This is a longstanding open problem, and even in the irrotational case there are only partial results relying on sign conditions or smallness assumptions. As a corollary, we obtain a relatively complete classification of solitary waves: they must be supercritical, symmetric, and monotonically decreasing on either side of a central crest. The proof introduces a new function which is related to the so-called flow force and has several surprising properties. In addition to solitary waves, our nonexistence result applies to “half-solitary” waves (e.g. bores) which decay in only one direction.

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30

Yamashita, Kei, and Taro Kakinuma. "PROPERTIES OF SURFACE AND INTERNAL SOLITARY WAVES." Coastal Engineering Proceedings 1, no. 34 (October 30, 2014): 45. http://dx.doi.org/10.9753/icce.v34.waves.45.

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31

Synolakis, Costas Emmanuel. "The runup of solitary waves." Journal of Fluid Mechanics 185 (December 1987): 523–45. http://dx.doi.org/10.1017/s002211208700329x.

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This is a study of the runup of solitary waves on plane beaches. An approximate theory is presented for non-breaking waves and an asymptotic result is derived for the maximum runup of solitary waves. A series of laboratory experiments is described to support the theory. It is shown that the linear theory predicts the maximum runup satisfactorily, and that the nonlinear theory describes the climb of solitary waves equally well. Different runup regimes are found to exist for the runup of breaking and non-breaking waves. A breaking criterion is derived for determining whether a solitary wave will break as it climbs up a sloping beach, and a different criterion is shown to apply for determining whether a wave will break during rundown. These results are used to explain some of the existing empirical runup relationships.

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32

Shen, Yuan, Bo Tian, Chong-Dong Cheng, and Tian-Yu Zhou. "Pfaffian solutions and nonlinear waves of a (3 + 1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt system in fluid mechanics." Physics of Fluids 35, no. 2 (February 2023): 025103. http://dx.doi.org/10.1063/5.0135174.

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Fluid mechanics is concerned with the behavior of liquids and gases at rest or in motion, where the nonlinear waves and their interactions are important. Hereby, we study a (3 + 1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt system in fluid mechanics. We determine a bilinear form of that system via the Hirota method. Nth-order Pfaffian solutions are obtained via the Pfaffian technique and our bilinear form, where N is a positive integer. Based on the Nth-order Pfaffian solutions, we derive the N-soliton, higher-order breather, and hybrid solutions. Using those solutions, we present the (1) elastic interaction between the two solitary waves with a short stem, (2) elastic interaction between the two solitary waves with a long stem, (3) fission between the two solitary waves, (4) fusion between the two solitary waves, (5) one breather wave, (6) elastic interaction between the two breather waves, (7) fission between the two breather waves, (8) fusion among the one breather wave and two solitary waves, and (9) elastic interaction between the one breather wave and one solitary wave.

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33

Nakamura, Y., and K. Ohtani. "Solitary waves in an ion-beam-plasma system." Journal of Plasma Physics 53, no. 2 (April 1995): 235–43. http://dx.doi.org/10.1017/s0022377800018146.

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Solitary waves in an ion-beam-plasma system are investigated theoretically using the pseudo-potential method, including finite temperatures of plasma ions and beam ions. The beam velocity is high enough to avoid ion-ion instability. Three kinds of solitary waves are possible, corresponding to ion- acoustic waves and to fast and slow space-charge waves in the beam. To observe the formation of solitary waves from an initial positive pulse, numerical simulations are performed. For the slow beam mode, a smaller solitary wave appears at the leading part of the pulse, which is a result of negative nonlinearity and anomalous dispersion of the slow mode, and is the opposite behaviour to the cases of the ion-acoustic wave and to the fast beam mode. Overtaking collisions of a solitary wave with a fast-mode solitary wave or with a slow-mode solitary wave are simulated.

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34

LIU, ZHENGRONG, and JIBIN LI. "BIFURCATIONS OF SOLITARY WAVES AND DOMAIN WALL WAVES FOR KdV-LIKE EQUATION WITH HIGHER ORDER NONLINEARITY." International Journal of Bifurcation and Chaos 12, no. 02 (February 2002): 397–407. http://dx.doi.org/10.1142/s0218127402004425.

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Bifurcations of solitary waves and domain wall waves for a KdV-like equation with higher order nonlinearity are studied, by using bifurcation theory of planar dynamical systems. Bifurcation parameter sets are shown. Numbers of solitary waves and domain wall waves are given. Under some parameter conditions, a lot of explicit formulas of solitary wave solutions and domain wall solutions are obtained.

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35

CHAMPNEYS, ALAN R., and MARK D. GROVES. "A global investigation of solitary-wave solutions to a two-parameter model for water waves." Journal of Fluid Mechanics 342 (July 10, 1997): 199–229. http://dx.doi.org/10.1017/s0022112097005193.

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The model equationformula herearises as the equation for solitary-wave solutions to a fifth-order long-wave equation for gravity–capillary water waves. Being Hamiltonian, reversible and depending upon two parameters, it shares the structure of the full steady water-wave problem. Moreover, all known analytical results for local bifurcations of solitary-wave solutions to the full water-wave problem have precise counterparts for the model equation.At the time of writing two major open problems for steady water waves are attracting particular attention. The first concerns the possible existence of solitary waves of elevation as local bifurcation phenomena in a particular parameter regime; the second, larger, issue is the determination of the global bifurcation picture for solitary waves. Given that the above equation is a good model for solitary waves of depression, it seems natural to study the above issues for this equation; they are comprehensively treated in this article.The equation is found to have branches of solitary waves of elevation bifurcating from the trivial solution in the appropriate parameter regime, one of which is described by an explicit solution. Numerical and analytical investigations reveal a rich global bifurcation picture including multi-modal solitary waves of elevation and depression together with interactions between the two types of wave. There are also new orbit-flip bifurcations and associated multi-crested solitary waves with non-oscillatory tails.

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YANG, T. S., and T. R. AKYLAS. "On asymmetric gravity–capillary solitary waves." Journal of Fluid Mechanics 330 (January 10, 1997): 215–32. http://dx.doi.org/10.1017/s0022112096003643.

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Symme tric gravity–capillary solitary waves with decaying oscillatory tails are known to bifurcate from infinitesimal periodic waves at the minimum value of the phase speed where the group velocity is equal to the phase speed. In the small-amplitude limit, these solitary waves may be interpreted as envelope solitons with stationary crests and are described by the nonlinear Schrödinger (NLS) equation to leading order. In line with this interpretation, it would appear that one may also co nstruct asymmetric solitary waves by shifting the carrier oscillations relative to the envelope of a symmetric solitary wave. This possibility is examined here on the basis of the fifth-order Korteweg–de Vries (KdV) equation, a model for g ravity–capillary waves on water of finite depth when the Bond number is close to 1/3. Using techniques of exponential asymptotics beyond all orders of the NLS theory, it is shown that asymmetric solitary waves of the form suggested by the NLS theory in fact are not possible. On the other hand, an infinity of symmetric and asymmetric solitary-wave solution families comprising two or more NLS solitary wavepackets bifurcate at finite values of the amplitude parameter. The asymptotic results are consistent with numerical solutions of the fifth-order KdV equation. Moreover, the asymptotic theory suggests that such multi-packet gravity–capillary solitary waves also exist in the full water-wave problem near the minimum of t he phase speed.

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37

Wang, Zhan, Emilian I. Părău, Paul A. Milewski, and Jean-Marc Vanden-Broeck. "Numerical study of interfacial solitary waves propagating under an elastic sheet." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2168 (August 8, 2014): 20140111. http://dx.doi.org/10.1098/rspa.2014.0111.

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Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a fully nonlinear thin shell model. Fully localized solitary waves are computed via a boundary integral method. Progression along the various branches of solutions shows that barotropic (i.e. surface modes) wave-packet solitary wave branches end with the free surface approaching the interface. On the other hand, the limiting configurations of long baroclinic (i.e. internal) solitary waves are characterized by an infinite broadening in the horizontal direction. Baroclinic wave-packet modes also exist for a large range of amplitudes and generalized solitary waves are computed in a case of a long internal mode in resonance with surface modes. In contrast to the pure gravity case (i.e without an elastic cover), these generalized solitary waves exhibit new Wilton-ripple-like periodic trains in the far field.

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38

Synolakis, Costas Emmanuel. "ARE SOLITARY WAVES THE LIMITING WAVES IN LONG WAVE RUNUP?" Coastal Engineering Proceedings 1, no. 21 (January 29, 1988): 14. http://dx.doi.org/10.9753/icce.v21.14.

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This is a study of the maximum runup of single long waves on plane beaches. Laboratory data are presented that suggest that solitary waves attain the higher runup distances than other single long waves with identical generation characteristics, such as energy or momentum. These results suggest that solitary waves may provide a limiting condition for long wave runup on plane beaches.

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39

Hirata, M., S. Okino, and H. Hanazaki. "Radiation of short waves from the resonantly excited capillary–gravity waves." Journal of Fluid Mechanics 810 (November 24, 2016): 5–24. http://dx.doi.org/10.1017/jfm.2016.702.

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Capillary–gravity waves resonantly excited by an obstacle (Froude number: $Fr=1$) are investigated by the numerical solution of the Euler equations. The radiation of short waves from the long nonlinear waves is observed when the capillary effects are weak (Bond number: $Bo<1/3$). The upstream-advancing solitary wave radiates a short linear wave whose phase velocity is equal to the solitary waves and group velocity is faster than the solitary wave (soliton radiation). Therefore, the short wave is observed upstream of the foremost solitary wave. The downstream cnoidal wave also radiates a short wave which propagates upstream in the depression region between the obstacle and the cnoidal wave. The short wave interacts with the long wave above the obstacle, and generates a second short wave which propagates downstream. These generation processes will be repeated, and the number of wavenumber components in the depression region increases with time to generate a complicated wave pattern. The upstream soliton radiation can be predicted qualitatively by the fifth-order forced Korteweg–de Vries equation, but the equation overestimates the wavelength since it is based on a long-wave approximation. At a large Bond number of $Bo=2/3$, the wave pattern has the rotation symmetry against the pattern at $Bo=0$, and the depression solitary waves propagate downstream.

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40

Derzho, Oleg G. "Brief communication: Multiscaled solitary waves." Nonlinear Processes in Geophysics 24, no. 4 (November 23, 2017): 695–700. http://dx.doi.org/10.5194/npg-24-695-2017.

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Abstract. It is analytically shown how competing nonlinearities yield multiscaled structures for internal solitary waves in stratified shallow fluids. These solitary waves only exist for large amplitudes beyond the limit of applicability of the Korteweg–de Vries (KdV) equation or its usual extensions. The multiscaling phenomenon exists or does not exist for almost identical density profiles. The trapped core inside the wave prevents the appearance of such multiple scales within the core area. The structural stability of waves of large amplitudes is briefly discussed. Waves of large amplitudes displaying quadratic, cubic and higher-order nonlinear terms have stable and unstable branches. Multiscaled waves without a vortex core are shown to be structurally unstable. It is anticipated that multiscaling phenomena will exist for solitary waves in various physical contexts.

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Khaled, Mahmood A. H., Ibrahim G. H. Loqman, and Kauther I. Alkuhlani. "PROPAGATION OF ION ACOUSTIC WAVES IN A MAGNETIZED QUANTUM PLASMA IN THE PRESENCE OF EXCHANGE-CORRELATION EFFECTS." Electronic Journal of University of Aden for Basic and Applied Sciences 3, no. 2 (June 30, 2022): 84–92. http://dx.doi.org/10.47372/ejua-ba.2022.2.156.

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The nonlinear propagation of ion acoustic solitary waves are studied in a magnetized quantum plasma consisting of cold inertia ions and inertialless quantum electrons and positrons, including exchange-correlation effects., A Zakharov-Kuznetsov equation is derived by using the reductive perturbation method. The effects of quantum plasma parameters on the propagation characteristics of the ion acoustic solitary waves have been investigated. It is found that the phase velocity, amplitude and width of the solitary waves are significantly affected by the presence of exchange-correlation potentials of electron and positron. Only solitary wave width effected by both quantum diffraction and magnetic field strength. The width of the solitary waves increases with the increase of both the quantum diffraction and magnetic field strength. The increase in the positron concentration causes to diminish both the solitary waves amplitude and width. The current results may be useful to understand the properties of ion acoustic waves propagating in dense space plasma environments where the quantum effects are expected to dominate.

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LAMB, KEVIN G. "Shoaling solitary internal waves: on a criterion for the formation of waves with trapped cores." Journal of Fluid Mechanics 478 (March 10, 2003): 81–100. http://dx.doi.org/10.1017/s0022112002003269.

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Shoaling solitary internal waves are ubiquitous features in the coastal regions of the world's oceans where waves with a core of recirculating fluid (trapped cores) can provide an effective transport mechanism. Here, numerical evidence is presented which suggests that there is a close connection between the limiting behaviour of large-amplitude solitary waves and the formation of such waves via shoaling. For some background states, large-amplitude waves are broad, having a nearly horizontal flow in their centre. The flow in the centre of such waves is called a conjugate flow. For other background states, large-amplitude waves can reach the breaking limit, at which the maximum current in the wave is equal to the wave's propagation speed. The presence of a background current with near-surface vorticity of the same sign as that induced by the wave can change the limiting behaviour from the conjugate-flow limit to the breaking limit. Numerical evidence is presented here which suggests that if large solitary waves cannot reach the breaking limit in the shallow water, that is if the background flow has a conjugate flow, then waves with trapped cores will not be formed via shoaling. It is also shown that, due to a change in the limiting behaviour of large waves, an appropriate background current can enable the formation of waves with trapped cores in stratifications for which such waves are not formed in the absence of a background current.

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Milewski, Paul A., and Zhan Wang. "Transversally periodic solitary gravity–capillary waves." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2161 (January 8, 2014): 20130537. http://dx.doi.org/10.1098/rspa.2013.0537.

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When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two- and three-dimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravity–capillary solitary waves are found to be of either elevation or depression type, tend to plane waves below a critical transverse period and tend to solitary lumps as the transverse period tends to infinity. The waves are found numerically in a Hamiltonian system for water waves simplified by a cubic truncation of the Dirichlet-to-Neumann operator. This approximation has been proved to be very accurate for both two- and three-dimensional computations of fully localized gravity–capillary solitary waves. The stability properties of these waves are then investigated via the time evolution of perturbed wave profiles.

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Gavrilov, N., V. Liapidevskii, and K. Gavrilova. "Mass and momentum transfer by solitary internal waves in a shelf zone." Nonlinear Processes in Geophysics 19, no. 2 (April 3, 2012): 265–72. http://dx.doi.org/10.5194/npg-19-265-2012.

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Abstract. The evolution of large amplitude internal waves propagating towards the shore and more specifically the run up phase over the "swash" zone is considered. The mathematical model describing the generation, interaction, and decaying of solitary internal waves of the second mode in the interlayer is proposed. The exact solution specifying the shape of solitary waves symmetric with respect to the unperturbed interface is constructed. It is shown that, taking into account the friction on interfaces in the mathematical model, it is possible to describe adequately the change in the phase and amplitude characteristics of two solitary waves moving towards each other before and after their interaction. It is demonstrated that propagation of large amplitude solitary internal waves of depression over a shelf could be simulated in laboratory experiments by internal symmetric solitary waves of the second mode.

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Pickett, J. S., L. J. Chen, S. W. Kahler, O. Santolík, M. L. Goldstein, B. Lavraud, P. M. E. Décréau, et al. "On the generation of solitary waves observed by Cluster in the near-Earth magnetosheath." Nonlinear Processes in Geophysics 12, no. 2 (February 2, 2005): 181–93. http://dx.doi.org/10.5194/npg-12-181-2005.

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Abstract. Through case studies involving Cluster waveform observations, solitary waves in the form of bipolar and tripolar pulses have recently been found to be quite abundant in the near-Earth dayside magnetosheath. We expand on the results of those previous studies by examining the distribution of solitary waves from the bow shock to the magnetopause using Cluster waveform data. Cluster's orbit allows for the measurement of solitary waves in the magnetosheath from about 10 RE to 19.5 RE. Our results clearly show that within the magnetosheath, solitary waves are likely to be observed at any distance from the bow shock and that this distance has no dependence on the time durations and amplitudes of the solitary waves. In addition we have found that these same two quantities show no dependence on either the ion velocity or the angle between the ion velocity and the local magnetic field direction. These results point to the conclusion that the solitary waves are probably created locally in the magnetosheath at multiple locations, and that the generation mechanism is most likely not solely related to ion dynamics, if at all. To gain insight into a possible local generation mechanism, we have examined the electron differential energy flux characteristics parallel and perpendicular to the magnetic field, as well as the local electron plasma and cyclotron frequencies and the type of bow shock that Cluster is behind, for several time intervals where solitary waves were observed in the magnetosheath. We have found that solitary waves are most likely to be observed when there are counterstreaming (~parallel and anti-parallel to the magnetic field) electrons at or below about 100eV. However, there are times when these counterstreaming electrons are present when solitary waves are not. During these times the background magnetic field strength is usually very low (<10nT), implying that the amplitudes of the solitary waves, if present, would be near or below those of other waves and electrostatic fluctuations in this region making it impossible to isolate or clearly distinguish them from these other emissions in the waveform data. Based on these results, we have concluded that some of the near-Earth magnetosheath solitary waves, perhaps in the form of electron phase-space holes, may be generated locally by a two-stream instability involving electrons based on the counterstreaming electrons that are often observed when solitary waves are present. We have not ruled out the possibility that the solitary waves could be generated as a result of the lower-hybrid Buneman instability in the presence of an electron beam, through the electron acoustic mode or through processes involving turbulence, which is almost always present in the magnetosheath, but these will be examined in a more comprehensive study in the future.

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Zhang, Weiguo, Xu Chen, Zhengming Li, and Haiyan Zhang. "Orbital Stability of Solitary Waves for Generalized Symmetric Regularized-Long-Wave Equations with Two Nonlinear Terms." Journal of Applied Mathematics 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/963987.

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This paper investigates the orbital stability of solitary waves for the generalized symmetric regularized-long-wave equations with two nonlinear terms and analyzes the influence of the interaction between two nonlinear terms on the orbital stability. SinceJis not onto, Grillakis-Shatah-Strauss theory cannot be applied on the system directly. We overcome this difficulty and obtain the general conclusion on orbital stability of solitary waves in this paper. Then, according to two exact solitary waves of the equations, we deduce the explicit expression of discriminationd′′(c)and give several sufficient conditions which can be used to judge the orbital stability and instability for the two solitary waves. Furthermore, we analyze the influence of the interaction between two nonlinear terms of the equations on the wave speed interval which makes the solitary waves stable.

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Wu, Yun, and Zhengrong Liu. "Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation." Advances in Mathematical Physics 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/812120.

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We study the bifurcation phenomena of nonlinear waves described by a generalized Zakharov-Kuznetsov equationut+au2+bu4ux+γuxxx+δuxyy=0. We reveal four kinds of interesting bifurcation phenomena. The first kind is that the low-kink waves can be bifurcated from the symmetric solitary waves, the 1-blow-up waves, the tall-kink waves, and the antisymmetric solitary waves. The second kind is that the 1-blow-up waves can be bifurcated from the periodic-blow-up waves, the symmetric solitary waves, and the 2-blow-up waves. The third kind is that the periodic-blow-up waves can be bifurcated from the symmetric periodic waves. The fourth kind is that the tall-kink waves can be bifurcated from the symmetric periodic waves.

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LIU, RUI, and WEIFANG YAN. "SOME COMMON EXPRESSIONS AND NEW BIFURCATION PHENOMENA FOR NONLINEAR WAVES IN A GENERALIZED mKdV EQUATION." International Journal of Bifurcation and Chaos 23, no. 03 (March 2013): 1330007. http://dx.doi.org/10.1142/s0218127413300073.

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Using the bifurcation method of dynamical systems, we study nonlinear waves in the generalized mKdV equation ut + a(1 + bu2)u2ux + uxxx = 0. (i) We obtain four types of new expressions. The first type is composed of four common expressions of the symmetric solitary waves, the kink waves and the blow-up waves. The second type includes four common expressions of the anti-symmetric solitary waves, the kink waves and the blow-up waves. The third type is made of two trigonometric expressions of periodic-blow-up waves. The fourth type is composed of two fractional expressions of 1-blow-up waves. (ii) We point out that there are two sets of kink waves which are called tall-kink waves and low-kink waves, respectively. (iii) We reveal two kinds of new bifurcation phenomena. The first phenomenon is that the low-kink waves can be bifurcated from four types of nonlinear waves, the symmetric solitary waves, blow-up waves, tall-kink waves and anti-symmetric solitary waves. The second phenomenon is that the 1-blow-up waves can be bifurcated from the periodic-blow-up waves. We also show that the common expressions include many results given by pioneers.

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NAKAYAMA, Keisuke, Taro KAKINUMA, Hidekazu TSUJI, and Masayuki OIKAWA. "Large Amplitude Internal Solitary Waves due to Solitary Resonance." Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering) 67, no. 2 (2011): I_6—I_10. http://dx.doi.org/10.2208/kaigan.67.i_6.

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LAGET, O., and F. DIAS. "Numerical computation of capillary–gravity interfacial solitary waves." Journal of Fluid Mechanics 349 (October 25, 1997): 221–51. http://dx.doi.org/10.1017/s0022112097006861.

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Two types of capillary–gravity interfacial solitary waves are computed numerically: ‘classical’ solitary waves which bifurcate from a uniform flow at a critical value of the velocity and solitary waves in the form of wave packets which bifurcate from a train of infinitesimal periodic waves with equal phase and group velocities. The effects of finite amplitude are shown to be quite different from the pure gravity case for the classical solitary waves. The solitary waves in the form of wave packets, which are known to exist for small density ratios, are shown to exist even for larger density ratios, but only at finite amplitude. The numerical code is based on an integro-differential formulation of the full Euler equations. The experimental results of Koop & Butler (1981), which have been compared earlier with results from model equations, are compared with the present numerical results.

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Journal articles on the topic 'Solitary waves'

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