Relevant bibliographies by topics / Nonlinear wave theories

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Nonlinear wave theories'

Author: Grafiati
Published: 28 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Nonlinear wave theories"

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Johnson, R. S. "Edge waves: theories past and present." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 365, no. 1858 (March 13, 2007): 2359–76. http://dx.doi.org/10.1098/rsta.2007.2013.

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The problem of edge waves as an example within classical water-wave theory is described by presenting an overview of some of the theories that have been offered for this phenomenon. The appropriate governing equations and boundary conditions are formulated, and then the important discoveries of Stokes and Ursell, concerning the travelling edge wave, are presented. (We do not address the corresponding problem of standing waves.) Thus, the linear problem and its spectrum are constructed; in addition, we also present the linear long-wave approximation to the problem, as well as Whitham's weakly nonlinear extension to Stokes' original theory. All these discussions are based on the same formulation of the problem, allowing an immediate comparison of the results, whether this be in terms of different approximations or whether the theory be for an irrotational flow or not. Gerstner's exact solution of the water-wave problem is then briefly described, together with a transformation that produces an exact solution of the full equations for the edge wave. The form of this solution is then used as the basis for a multiple-scale description of the edge wave over a slowly varying depth; this leads to a version of the shallow-water equations which has an exact solution that corresponds to the edge wave. Some examples of the theoretical predictions for the run-up pattern are presented. We conclude with three variants of nonlinear model equations that may prove useful in the study of edge waves and, particularly, the interaction of different modes.
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Hardy, Thomas A., and Nicholas C. Kraus. "COUPLING STOKES AND CNOIDAL WAVE THEORIES IN A NONLINEAR REFRACTION MODEL." Coastal Engineering Proceedings 1, no. 21 (January 29, 1988): 42. http://dx.doi.org/10.9753/icce.v21.42.

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An efficient numerical model is presented for calculating the refraction and shoaling of finite-amplitude waves over an irregular sea bottom. The model uses third-order Stokes wave theory in relatively deep water and second-order cnoidal wave theory in relatively shallow water. It can also be run using combinations of lower-order wave theories, including a pure linear wave mode. The problem of the connection of Stokes and cnoidal theories is investigated, and it is found that the use of second-order rather than first-order cnoidal theory greatly reduces the connection discontinuity. Calculations are compared with physical model measurements of the height and direction of waves passing over an elliptical shoal. The finite-amplitude wave model gives better qualitative and quantitative agreement with the measurements than the linear model.
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Zhang, Huichen, and Markus Brühl. "GENERATION OF EXTREME TRANSIENT WAVES IN EXPERIMENTAL MODELS." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 51. http://dx.doi.org/10.9753/icce.v36.waves.51.

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The transfer of natural waves and sea states into small- and large-scale model teste contributes to the proper design of offshore and coastal structure. Such shallow-water ocean surface waves are highly nonlinear and subject to wave transformation and nonlinear wave-wave interactions. However, the standard methods of wave generation according to conventional wave theories and wave analysis methods are limited to simple regular waves, simple sea states and low-order wave generation without considering the nonlinear wave-wave interactions. The research project Generation of Extreme Transient Waves in Experimental Models (ExTraWaG) aims to accurately generate target transient wave profile at a pre-defined position in the wave flume (transfer point) under shallow water conditions. For this purpose, the KdV-based nonlinear Fourier transform is introduced as a continuative wave analysis method and is applied to investigate the nonlinear spectral character of experimental wave data. Furthermore, the method is applied to generate transient nonlinear waves as specific locations in the wave flume, considering the nonlinear transformation and interactions of the propagating waves.
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Eldrup, Mads Røge, and Thomas Lykke Andersen. "Applicability of Nonlinear Wavemaker Theory." Journal of Marine Science and Engineering 7, no. 1 (January 14, 2019): 14. http://dx.doi.org/10.3390/jmse7010014.

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Generation of high-quality waves is essential when making numerical or physically model tests. When using a wavemaker theory outside the validity area, spurious waves are generated. In order to investigate the validity of different wave generation methods, new model test results are presented where linear and nonlinear wave generation theories are tested on regular and irregular waves. A simple modification to the second-order wavemaker theory is presented, which significantly reduces the generation of spurious waves when used outside its range of applicability. For highly nonlinear regular waves, only the ad-hoc unified wave generation based on stream function wave theory was found acceptable. For irregular waves, similar conclusions are drawn, but the modified second-order wavemaker method is more relevant. This is because the ad-hoc unified generation method for irregular waves requires the wave kinematics to be calculated by a numerical model, which might be quite time-consuming. Finally, a table is presented with the range of applicability for each wavemaker method for regular and irregular waves.
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RAVAL, ASHISH, XIANYUN WEN, and MICHAEL H. SMITH. "Numerical simulation of viscous, nonlinear and progressive water waves." Journal of Fluid Mechanics 637 (September 23, 2009): 443–73. http://dx.doi.org/10.1017/s002211200999070x.

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A numerical simulation is performed to study the velocity, streamlines, vorticity and shear stress distributions in viscous water waves with different wave steepness in intermediate and deep water depth when the average wind velocity is zero. The numerical results present evidence of ‘clockwise’ and ‘anticlockwise’ rotation of the fluid at the trough and crest of the water waves. These results show thicker vorticity layers near the surface of water wave than that predicted by the theories of inviscid rotational flow and the low Reynolds number viscous flow. Moreover, the magnitude of vorticity near the free surface is much larger than that predicted by these theories. The analysis of the shear stress under water waves show a thick shear layer near the water surface where large shear stress exists. Negative and positive shear stresses are observed near the surface below the crest and trough of the waves, while the maximum positive shear stress is inside the water and below the crest of the water wave. Comparison of wave energy decay rate in intermediate depth and deep water waves with laboratory and theoretical results are also presented.
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Vakakis, A. F. "Scattering of Structural Waves by Nonlinear Elastic Joints." Journal of Vibration and Acoustics 115, no. 4 (October 1, 1993): 403–10. http://dx.doi.org/10.1115/1.2930364.

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An analytic study of the scattering of structural waves by nonlinear elastic joints is presented. Under the assumption of small nonlinearities and/or amplitudes of motion, an averaging methodology is implemented for analyzing the interaction between an incident wave and a nonlinear joint with symmetric stiffness. It is found that, contrary to the predictions of existing linear theories, a single incident wave gives rise to an infinity of reflected waves with frequencies equal to odd multiples of the frequency of the incident wave. The orders of magnitude of the amplitudes of the various reflected waves are considered, and an application of the theory is made by considering the wave scattering from a joint with cubic stiffness nonlinearity. In addition, it is shown that the wave propagation approach presented in this work can be effectively used for predicting nonlinear free oscillations (standing waves) in finite waveguides with nonlinear joints.
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Liu, C. M., H. H. Hwung, and R. Y. Yang. "The Consistence Between the Stokes Wave Theory and General Wave Theory." Journal of Mechanics 25, no. 3 (September 2009): N17—N20. http://dx.doi.org/10.1017/s172771910000280x.

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AbstractThe consistence between the Stokes wave theory and general wave theory is examined in this study. As well known, the nonlinear terms of Stokes wave are generated by the self-interaction of first-order wave. On the other side, using the general wave theory one can also obtain the nonlinear solutions according to the interaction of n waves with the same amplitude, frequency and phase. It is found that the inconsistence between these two wave trains arises due to the subharmonic effects included in general wave theory but not considered in the Stokes theory. In conclusion, these two theories are substantially different unless the Bernoulli constants are properly chosen for mathematical equivalence.
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Engelbrecht, J., and M. Braun. "Nonlinear Waves in Nonlocal Media." Applied Mechanics Reviews 51, no. 8 (August 1, 1998): 475–88. http://dx.doi.org/10.1115/1.3099016.

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This review article gives a brief overview on nonlocal theories in solid mechanics from the viewpoint of wave motion. The influence of two essential qualities of solids—nonlocality and nonlinearity—is discussed. The effects of microstructure are analyzed in order to understand their role in nonlocal theories. The various models are specified on the level of one-dimensional unidirectional motion in order to achieve mathematical clarity of interpreting physical phenomena. Three main types of evolution equations are shown to govern deformation waves under such assumptions. Based on the dispersion analysis, weak, true, and strong nonlocalities are distinguished. There are 75 references included with this article.
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Elfouhaily, Tanos, D. R. Thompson, D. Vandemark, and B. Chapron. "Truncated Hamiltonian versus surface perturbation in nonlinear wave theories." Waves in Random Media 10, no. 1 (January 2000): 103–16. http://dx.doi.org/10.1088/0959-7174/10/1/308.

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Noonan, Julie, and Roger Smith. "Linear and weakly nonlinear internal wave theories applied to "morning glory" waves." Geophysical & Astrophysical Fluid Dynamics 33, no. 1 (1985): 123–43. http://dx.doi.org/10.1080/03091928508240749.

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Dissertations / Theses on the topic "Nonlinear wave theories"

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Girard, Réjean. "Relativistic nonlinear wave equations with groups of internal symmetry." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75688.

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A nonlinear wave equation invariant with respect to unitary representations of the Lorentz group is considered in an attempt to describe extended particles with spin and positive definite energy by means of a self-confined classical field. The wave function has an infinite number of components and, in the specific representations used, the corresponding internal degree of freedom is identified with the spin. A fractional power of the scalar bilinear invariant appears as an appropriate choice for the nonlinearity in order that all the stationary states be localized. Two approximation methods are proposed and both lead to results that bear a resemblance to the results of the MIT bag model.
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Hoseini, Sayed Mohammad. "Solitary wave interaction and evolution." Access electronically, 2007. http://www.library.uow.edu.au/adt-NWU/public/adt-NWU20080221.110619/index.html.

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Kim, Won-Gyu 1962. "A Study of Nonlinear Dynamics in an Internal Water Wave Field in a Deep Ocean." Thesis, University of North Texas, 1996. https://digital.library.unt.edu/ark:/67531/metadc278092/.

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The Hamiltonian of a stably stratified incompressible fluid in an internal water wave in a deep ocean is constructed. Studying the ocean internal wave field with its full dynamics is formidable (or unsolvable) so we consider a test-wave Hamiltonian to study the dynamical and statistical properties of the internal water wave field in a deep ocean. Chaos is present in the internal test-wave dynamics using actual coupling coefficients. Moreover, there exists a certain separatrix net that fills the phase space and is covered by a thin stochastic layer for a two-triad pure resonant interaction. The stochastic web implies the existence of diffusion of the Arnold type for the minimum dimension of a non-integrable autonomous system. For non-resonant case, stochastic layer is formed where the separatrix from KAM theory is disrupted. However, the stochasticity does not increase monotonically with increasing energy. Also, the problem of relaxation process is studied via microscopic Hamiltonian model of the test-wave interacting nonlinearly with ambient waves. Using the Mori projection technique, the projected trajectory of the test-wave is transformed to a form which corresponds to a generalized Langevin equation. The mean action of the test-wave grows ballistically for a short time regime, and quenches back to the normal diffusion for a intermediate time regime and regresses linearly to a state of statistical equilibrium. Applying the Nakajima-Zwanzig technique on the test-wave system, we get the generalized master equation on the test-wave system which is non-Markovian in nature. From our numerical study, the distribution of the test-wave has non-Gaussian statistics.
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Narisetti, Raj K. "Wave propagation in nonlinear periodic structures." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/39643.

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A periodic structure consists of spatially repeating unit cells. From man-made multi-span bridges to naturally occurring atomic lattices, periodic structures are ubiquitous. The periodicity can be exploited to generate frequency bands within which elastic wave propagation is impeded. A limitation to the linear periodic structure is that the filtering properties depend only on the structural design and periodicity which implies that the dispersion characteristics are fixed unless the overall structure or the periodicity is altered. The current research focuses on wave propagation in nonlinear periodic structures to explore tunability in filtering properties such as bandgaps, cut-off frequencies and response directionality. The first part of the research documents amplitude-dependent dispersion properties of weakly nonlinear periodic media through a general perturbation approach. The perturbation approach allows closed-form estimation of the effects of weak nonlinearities on wave propagation. Variation in bandstructure and bandgaps lead to tunable filtering and directional behavior. The latter is due to anisotropy in nonlinear interaction that generates low response regions, or "dead zones," within the structure.The general perturbation approach developed has also been applied to evaluate dispersion in a complex nonlinear periodic structure which is discretized using Finite Elements. The second part of the research focuses on wave dispersion in strongly nonlinear periodic structures which includes pre-compressed granular media as an example. Plane wave dispersion is studied through the harmonic balance method and it is shown that the cut-off frequencies and bandgaps vary significantly with wave amplitude. Acoustic wave beaming phenomenon is also observed in pre-compressed two-dimensional hexagonally packed granular media. Numerical simulations of wave propagation in finite lattices also demonstrated amplitude-dependent bandstructures and directional behavior so far observed.
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Franz, David, and University of Lethbridge Faculty of Arts and Science. "Turing patterns in linear chemical reaction systems with nonlinear cross diffusion." Thesis, Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2007, 2007. http://hdl.handle.net/10133/659.

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Turing patterns have been studied for over 50 years as a pattern forming mechanism. To date the current focus has been on the reaction mechanism, with little to no emphasis on the diffusion terms. This work focuses on combining the simplest reaction mechanism possible and the use of nonlinear cross diffusion to form Turing patterns. We start by using two methods of bifurcation analysis to show that our model can form a Turing instability. A diffusion model (along with some variants) is then presented along with the results of numerical simulations. Various tests on both the numerical methods and the model are done to ensure the accuracy of the results. Finally an additional model that is closed to mass flow is introduced along with preliminary results.
vi, 55 leaves : ill. ; 29 cm.
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Kuechler, Sebastian. "Wave Propagation in an Elastic Half-Space with Quadratic Nonlinearity." Thesis, Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19823.

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This study investigates wave propagation in an elastic half-space with quadratic nonlinearity due to a line load on the surface. The consideration of this problem is one of the well known Lamb problems. Even since Lamb's original solution, numerous investigators have obtained solutions to many different variants of the Lamb problem. However, most of the solutions existing in the current literature are limited to wave propagation in a linear elastic half-space. In this work, the Lamb problem in an elastic half-space with quadratic nonlinearity is considered. For this, the problem is first formulated as a hyperbolic system of conservation laws, which is then solved numerically using a semi-discrete central scheme. The numerical method is implemented using the package CentPack. The accuracy of the numerical method is first studied by comparing the numerical solution with the analytical solution for a half-space with linear response (the original Lamb's problem). The numerical results for the half-space with quadratic nonlinearity are than studied using signal-processing tools such as the fast Fourier transform (FFT) in order to analyze and interpret any nonlinear effects. This in particular gives the possibility to evaluate the excitation of higher order harmonics whose amplitude is used to infer material properties. To quantify and compare the nonlinearity of different materials, two parameters are introduced; these parameters are similar to the acoustical nonlinearity parameter for plane waves.
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Kupčíková, Laura. "Částice plovoucí na volné hladině vln." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-444637.

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This master’s thesis deals with analytical and numerical description of surface gravity waves. Wave theories and their influence on water particle movement is described in the theoretical part of the thesis. Water particle moves in the same direction as wave propagation and this phenomenon is called Stokes drift. It has a significant influence on sediment transport and floating particle movement at water free surface. The experimental part consists of wave profile monitoring and water particle tracking in a wave flume with wave generator and beach model. The experimental results are compared with numerical simulation performed in the ANSYS Fluent software. Finally, the wave profiles obtained from simulation are compared with experimental wave profiles extracted by digital image processing.
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Braun, Michael Rainer. "Characterization of nonlinearity parameters in an elastic material with quadratic nonlinearity with a complex wave field." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26566.

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Thesis (M. S.)--Civil and Environmental Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Jacobs, Laurence; Committee Co-Chair: Qu, Jianmin; Committee Member: DesRoches, Reginald. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Aceves, Alejandro Borbolla. "Snell's laws at the interface between nonlinear dielectrics." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184467.

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A theory is presented which describes the global reflection and transmission characteristics of a self-focused channel propagating at an oblique angle of incidence to an interface separating two or more self-focusing nonlinear dielectric media. A complete characterization of the different behavior of the channel is given in the proper parameter space. In the dominant region, the nonlinear wavepacket representing the self-focused channel is represented as an equivalent particle moving in an equivalent potential. The dynamics of the particle is described by Newton's equations of motion, with the asymptotic propagation paths of the channel being read off from the associated phase planes of the equivalent potential. This theory provides therefore, the nonlinear Snell's Laws of refleciton or transmission since the particle dynamics gives the critical angle of total reflection and in the case of transmission, the corresponding angle of transmission. This theory also gives the stability characteristics of nonlinear surface waves, which had only been partially established in the past through numerical simulations. Finally, some applications of the theory are presented such as the design of an all-optical power adjustable spatial scanning element and an all optical switch. Extensions of the theory to waveguides with multiple interfaces are also given and possible new directions are also suggested.
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Ohm, Won-suk. "Effects of dispersion on nonlinear surface acoustic waves in substrates laminated with films /." Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3038194.

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Books on the topic "Nonlinear wave theories"

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Kichenassamy, Satyanad. Nonlinear wave equations. New York: M. Dekker, 1996.

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NATO Advanced Research Workshop on Nonlinear Wave Processes in Excitable Media (1989 Leeds, England). Nonlinear wave processes in excitable media. New York: Plenum Press, 1991.

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Toda, Morikazu. Nonlinear waves and solitons. London: Kluwer, 1989.

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Shen, Samuel S. A course on nonlinear waves. Dordrecht: Springer, 1993.

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Baumgartel, Klaus. Topics on nonlinear wave-plasma interaction. Basel: Birkhaüser Verlag, 1987.

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Baumgartel, Klaus. Topics on nonlinear wave-plasma interaction. Basel: Birkhauser Verlag, 1987.

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Sulem, C. The nonlinear Schrödinger equation: Self-focusing and wave collapse. New York: Springer, 1999.

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Bonilla, L. L. Nonlinear wave methods for charge transport. Weinheim: Wiley-VCH, 2010.

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Lʹvov, V. S. Wave turbulence under parametric excitation: Applications to magnets. Berlin: Springer-Verlag, 1994.

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Pornsuwancharoen, N. Optical solitons in nonlinear micro ring resonators: Unexpected results and applications. Hauppauge, NY: Nova Science Publishers, 2009.

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Book chapters on the topic "Nonlinear wave theories"

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Sugimoto, Nobumasa, and Dai Shimizu. "Linear and Nonlinear Theories for Thermoacoustic Waves in a Gas Filled Tube Subject to a Temperature Gradient." In Applied Wave Mathematics II, 187–204. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-29951-4_9.

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Castagnino, Mario, Jorge Guerón, and Adolfo Ordoñez. "A theorem on wave packets." In Nonlinear Phenomena and Complex Systems, 159–67. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-1-4020-2149-7_9.

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Racke, Reinhard. "Global solutions to wave equations — existence theorems." In Lectures on Nonlinear Evolution Equations, 7–14. Wiesbaden: Vieweg+Teubner Verlag, 1992. http://dx.doi.org/10.1007/978-3-663-10629-6_2.

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Racke, Reinhard. "Global solutions to wave equations — existence theorems." In Lectures on Nonlinear Evolution Equations, 7–14. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-21873-1_2.

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Kenig, Carlos. "Universal Profiles and Rigidity Theorems for the Energy Critical Wave Equation." In Nonlinear Partial Differential Equations, 169–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25361-4_8.

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Raynovskyy, Ihor, and Alexander Timokha. "Nonlinear modal theories of nonparametric resonant waves in an upright circular container." In Sloshing in Upright Circular Containers, 55–86. First edition. | Boca Raton : CRC Press, 2020. |: CRC Press, 2020. http://dx.doi.org/10.1201/9780429356711-4.

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Kazakov, A. L., P. A. Kuznetsov, and A. A. Lempert. "On a Heat Wave for the Nonlinear Heat Equation: An Existence Theorem and Exact Solution." In Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy, 223–28. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38870-6_29.

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Selmi, Ridha, and Rim Nasfi. "Exponential Mixing and Ergodic Theorems for a Damped Nonlinear Wave Equation with Space-Time Localised Noise." In Trends in Mathematics, 221–29. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-04459-6_21.

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"Nonlinear Wave Theories." In Advanced Series on Ocean Engineering, 309–493. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774828_0006.

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Marghany, Maged. "Novel relativistic theories of ocean wave nonlinearity imagine mechanism in synthetic aperture radar." In Nonlinear Ocean Dynamics, 163–90. Elsevier, 2021. http://dx.doi.org/10.1016/b978-0-12-820785-7.00009-5.

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Conference papers on the topic "Nonlinear wave theories"

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Yim, Solomon C., Alfred R. Osborne, and Ali Mohtat. "Nonlinear Ocean Wave Models and Laboratory Simulation of High Seastates and Rogue Waves." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-62706.

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With the increasing demand for marine structures, including ships and wave energy devices, to operate in energetic, high seastates, the need for modeling and simulation of nonlinear ocean wave fields in large-scale wave basins is becoming essential. In response to this demand, a number of large-scale wave basins have been placed into operation over the years and larger and more sophisticated new ones are under planning and construction. In this article, the current state of practice and technical issues in modeling and simulation of high seastate ocean waves are summarized. A novel methodology for quantitative evaluation of the suitability of competing linear and nonlinear wave theories for a given wave field with multi-spatial measurements is presented. Preliminary results of an on-going study on wave modeling and analysis of measured data from a wave simulation performance study of the Oregon State University directional wave basin, using nonlinear wave theory (e.g. the nonlinear Schrödinger equation), nonlinear Fourier analysis and inference to the existence of rogue waves, are presented. Suggestions on future development of nonlinear wavemaker theories and numerical modeling and simulation of large-scale wave basin nonlinear wave generation are proposed. The article concludes with some observations and remarks on the importance of using an appropriate wave theory to determine the existence of nonlinear coherence structures, including breathers and rogue waves.
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Hua, Cun-cai. "On the Solitary Wave and Periodic Wave Solutions of the Nonlinear Drift-Wave Equation Arising from Magnetized Plasmas." In 2011 Fourth International Workshop on Chaos-Fractals Theories and Applications (IWCFTA). IEEE, 2011. http://dx.doi.org/10.1109/iwcfta.2011.47.

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Hardy, Thomas A., and Nicholas C. Kraus. "Coupling Stokes and Cnoidal Wave Theories in a Nonlinear Refraction Model." In 21st International Conference on Coastal Engineering. New York, NY: American Society of Civil Engineers, 1989. http://dx.doi.org/10.1061/9780872626874.043.

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Yan, Fang, and Haihong Liu. "Exact Travelling Wave Solutions and the Bifurcation for Nonlinear Evolution Modified ZK Equation." In 2010 International Workshop on Chaos-Fractals Theories and Applications (IWCFTA). IEEE, 2010. http://dx.doi.org/10.1109/iwcfta.2010.83.

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Khait, Anatoliy, and Lev Shemer. "Nonlinear Generation of Narrow-Banded Wave Trains." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-95364.

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Abstract Analytic method for nonlinear wave generation by a wavemaker that is somewhat different from the nonlinear theory of Schäffer is proposed. The method that is based on the Nonlinear Schrödinger (NLS) equation and the nonlinear boundary condition at the wavemaker is free of 2nd order limitation inherent to the existing wavemaker theories. Advantages offered by the NLS model allowed simplification of the expressions for determination of the wavemaker driving signal and thus made them easily applicable in practice. The nonlinear correction to the wavemaker driving signal is calculated from the complex surface elevation envelope obtained as a solution of the NLS equation at the prescribed location in the wave flume. The domain of applicability of the generation method was determined on the basis of numerous experiments in the wave flume. A very good generation of the required wave train shape was obtained for sufficiently narrow-banded wave trains.
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Schlo̸er, Signe, Henrik Bredmose, and Harry B. Bingham. "Irregular Wave Forces on Monopile Foundations: Effect of Full Nonlinearity and Bed Slope." In ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2011. http://dx.doi.org/10.1115/omae2011-49709.

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Forces on a monopile from a nonlinear irregular unidirectional wave model are investigated. Two seabed profiles of different slopes are considered. Morison’s equation is used to investigate the forcing from fully nonlinear irregular waves and to compare the results with those obtained from linear wave theory and with stream function wave theory. The latter of these theories is only valid on a flat bed. The three predictions of wave forces are compared and the influence of the bed slope is investigated. Force-profiles of two selected waves from the irregular wave train are further compared with the corresponding force-profiles from stream function theory. The results suggest that the nonlinear irregular waves give rise to larger extreme wave forces than those predicted by linear theory and that a steeper bed slope increases the wave forces both for linear and nonlinear waves. It is further found that stream function theory in some cases underestimate the wave forces acting on the monopile.
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Mohtat, Ali, Solomon C. Yim, Nasim Adami, and Pedro Lomonaco. "A General Nonlinear Wavemaker Theory for Intermediate- to Deep-Water Waves Using Inverse Scattering Transform." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-19359.

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Abstract Analysis and generation of (nonlinear) intermediate- to deep-water waves with large steepness in experimental facilities are some of the most challenging tasks in wave mechanics. The inherent instability of water waves in deep-water waves makes the linear-based wave generation and analysis less accurate and incapable of generating and characterizing correctly nonlinear behavior of the target wave field. In this presented research, a detailed assessment of the wavemaker theories and steps included in experimental approaches are presented. After establishing the nonlinear behavior of generated intermediate- to deep-water waves, a novel wavemaker theory based on the nonlinear Schrödinger equation is proposed. The implementation of the proposed wavemaker theory shows its capability of generating deep-water waves more accurately and preserving the correct order of nonlinearity.
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Liu, Yuming, Hongmei Yan, and Tin-Woo Yung. "Nonlinear Resonant Response of Deep Draft Platforms in Surface Waves." In ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/omae2010-20823.

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To minimize body motions, floating marine structures are often designed with natural frequencies far away from the spectrum of ocean waves. Such design considerations led to a class of deep draft caisson vessels (DDCV or spars). Even so, large resonant responses may still be generated by excitation from nonlinear interactions of waves with body motions. Past experiments indicated that a DDCV experiences large-amplitude heave and pitch resonant motions when the incident wave frequency is much larger than the heave and pitch natural frequencies. Such resonant motions are not predicted by classical theories without considering nonlinear effects. This nonlinear mechanism has received little attention because of the complex nonlinear wave-body dynamics involved. In this work, we investigate nonlinear wave-wave and wave-body interaction effects on dynamic instability of such marine structures. We first perform a linear stability analysis of the wave-frequency body motion. From the analysis, we find that at certain incident wave frequencies the body motion is unstable with natural heave and pitch motions growing exponentially with time by taking energy from the incident wave through nonlinear wave-body interactions. The condition for the occurrence of instability and the key characteristic features of unstable natural heave and pitch motions, predicted by the analysis, agree well with the experimental measurement and our full-nonlinear numerical simulations. As time-domain fully nonlinear numerical simulations are computationally expensive, we further develop an approximate time-domain analytic model, by including the second-order body nonlinearity only, for predicting the onset of instability and ultimate response of DDCVs in both regular and irregular waves. We use this model to systematically investigate the dependence of unstable motions on frequency detuning, damping, body geometry, and wave parameters.
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Chatziioannou, Konstantinos, Vanessa Katsardi, Apostolos Koukouselis, and Euripidis Mistakidis. "Nonlinear Dynamic Response of a Compliant Tower Under the Effect of Steady and Unsteady Sea States." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-62449.

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The purpose of this work is to highlight the importance of considering the actual nonlinear dynamic response for the analysis and design of fixed deep water platforms. The paper highlights the necessity of applying dynamic analysis through the comparison with the results obtained by the authors by applying static nonlinear analysis on the structure under examination. The example treated in the context of the present paper is a compliant tower, set-up in deep water. Nonlinearities are considered both for the calculation of the wave loadings and the structural analysis. The wave loading is based on linear random wave theory and comparisons are provided with the steady wave theories, Airy and Stokes 5th. The former solution is based on the most probable shape of a large linear wave on a given sea-state; the auto-correlation function of the underlying spectrum. On the other hand, in the field of structural analysis, two cases are considered for comparison, static analysis and time history dynamic analysis. For both types of analysis, two sub-cases are considered, a case in which geometric nonlinearity and nonlinearities related to the modelling of the soil are considered and a case in which the corresponding linear theories are employed (reference cases). The structural calculations were performed using the well-known structural analysis software SAP2000, which was enhanced by a special programming interface that was developed to calculate the wave loading and to directly apply the generated loads on the structural members. The results show that the consideration of the particle velocities associated with the linear random wave theory in the wave loading lead to significant differences with respect to the steady wave theories in terms of the displacements and stresses of the structure. Moreover, irrespectively of the adopted wave theory, the nonlinear analyses lead to significant discrepancies with respect to the linear ones. This is mainly associated with the nonlinear properties of the soil. Another source of discrepancies between the results of static and dynamic analyses stems from the change of the effective natural frequency of the structure when nonlinearities are considered.
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Lakitosh, F., and P. Ananthakrishnan. "Analysis of Ship Hull Plate Vibrations Induced by Wave and Slamming Loads." In ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/omae2012-83174.

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The hydroelasticity problem related to multi-hull ship plate vibrations excited by periodic and transient surface wave forces is analyzed. Theoretical method based on the Wagner theory and empirical methods based on classification society ABS rules are considered for determining the transient slamming force on the ship hull. A boundary integral method based on the simple source distribution (Yeung [1]) and mixed Eulerian and Lagrangian (MEL) formulation (Longuet-Higgins and Cokelet [2]) for the determination of the slamming force is in progress. A suite of plate theories, ranging from small-amplitude linear undamped isotropic plate theory to damped nonlinear, stiffened-plate theories, are considered to determine the vibrations of ship-hull plates subject to the wave forces. In the present work, finite-difference algorithms are developed to solve the nonlinear plate equations. Results for range of sea states and hull scantlings are obtained to determine key structural parameters affecting the structural integrity. The algorithms and the methodology developed can be used for efficient design of multi-hull ships, and perhaps also to update classification society rules on structural design.
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