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Journal articles on the topic 'Nonlinear field equations'

Author: Grafiati

Published: 18 May 2024

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1

Tan, Jinggang, Ying Wang, and Jianfu Yang. "Nonlinear fractional field equations." Nonlinear Analysis: Theory, Methods & Applications 75, no. 4 (March 2012): 2098–110. http://dx.doi.org/10.1016/j.na.2011.10.010.

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2

Fairlie, David B. "Interconnections among nonlinear field equations." Journal of Physics A: Mathematical and Theoretical 53, no. 10 (February 20, 2020): 104001. http://dx.doi.org/10.1088/1751-8121/ab6f17.

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3

Rego-Monteiro, M. A., and F. D. Nobre. "Nonlinear quantum equations: Classical field theory." Journal of Mathematical Physics 54, no. 10 (October 2013): 103302. http://dx.doi.org/10.1063/1.4824129.

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4

Tanaka, Yosuke, Takefumi Shudo, Tetsutaro Yosinaga, and Hiroshi Kimura. "Relativistic field equations and nonlinear dynamics." Chaos, Solitons & Fractals 37, no. 4 (August 2008): 941–49. http://dx.doi.org/10.1016/j.chaos.2008.01.004.

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5

Burt, P. B. "Nonperturbative solution of nonlinear field equations." Il Nuovo Cimento B 100, no. 1 (July 1987): 43–52. http://dx.doi.org/10.1007/bf02829775.

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6

Wells, R. O. "Nonlinear field equations and twistor theory." Mathematical Intelligencer 7, no. 2 (June 1985): 26–32. http://dx.doi.org/10.1007/bf03024171.

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7

Bruce, S. A. "Nonlinear Maxwell equations and strong-field electrodynamics." Physica Scripta 97, no. 3 (February 10, 2022): 035303. http://dx.doi.org/10.1088/1402-4896/ac50c2.

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Abstract We investigate two Lagrangian models of nonlinear electrodynamics (NLED). These models lead to two different sets of nonlinear (NL) Maxwell equations. The first case deals with the well-known Heisenberg-Euler (HE) model of electromagnetic (EM) self-interactions in a vacuum where only the lowest orders in EM Lorentz invariants are considered. The second instance proposes an extension of the HE model. It consists of a NL Maxwell-Dirac spinor model where the EM field modifies the dynamics of the energy-momentum operator sector of the Dirac Lagrangian instead of its rest-mass term counterpart. This work complements our recent research on NL Dirac equations in the strong EM field regime.

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8

Clapp, Mónica, and Tobias Weth. "Multiple Solutions of Nonlinear Scalar Field Equations." Communications in Partial Differential Equations 29, no. 9-10 (January 2, 2005): 1533–54. http://dx.doi.org/10.1081/pde-200037766.

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9

Mederski, Jarosław. "Nonradial solutions of nonlinear scalar field equations." Nonlinearity 33, no. 12 (October 23, 2020): 6349–80. http://dx.doi.org/10.1088/1361-6544/aba889.

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10

Liu, Jiu, Tao Liu, and Jia-Feng Liao. "A perturbation of nonlinear scalar field equations." Nonlinear Analysis: Real World Applications 45 (February 2019): 531–41. http://dx.doi.org/10.1016/j.nonrwa.2018.07.022.

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11

Jeanjean, Louis, and Sheng-Sen Lu. "Nonlinear scalar field equations with general nonlinearity." Nonlinear Analysis 190 (January 2020): 111604. http://dx.doi.org/10.1016/j.na.2019.111604.

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12

Edelen, Dominic G. B., and Jianhua Wang. "Transformation methods for solving nonlinear field equations." International Journal of Theoretical Physics 30, no. 6 (June 1991): 865–906. http://dx.doi.org/10.1007/bf00674028.

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13

Edelen, Dominic G. B. "Ideals and solutions of nonlinear field equations." International Journal of Theoretical Physics 29, no. 7 (July 1990): 687–737. http://dx.doi.org/10.1007/bf00673909.

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14

Grauel, A. "Nonlinear field equations and the Painlevé test." Chinese Physics Letters 3, no. 5 (May 1986): 201–4. http://dx.doi.org/10.1088/0256-307x/3/5/003.

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15

Burt, P. B., and T. J. Pickett. "Nonperturbative solution construction of nonlinear field equations." Lettere Al Nuovo Cimento Series 2 44, no. 7 (December 1985): 473–76. http://dx.doi.org/10.1007/bf02746743.

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16

Li, C. M., and Y. Y. Li. "Nonautonomous Nonlinear Scalar Field Equations in R2." Journal of Differential Equations 103, no. 2 (June 1993): 421–36. http://dx.doi.org/10.1006/jdeq.1993.1058.

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17

Bekova, G. T., and A. A. Zhadyranova. "MULTI-LINE SOLITON SOLUTIONS FOR THE TWO-DIMENSIONAL NONLINEAR HIROTA EQUATION." PHYSICO-MATHEMATICAL SERIES 2, no. 336 (April 15, 2021): 172–78. http://dx.doi.org/10.32014/2021.2518-1726.38.

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At present, the question of studying multidimensional nonlinear integrable equations in the framework of the theory of solitons is very interesting to foreign and Kazakh scientists. Many physical phenomena that occur in nature can be described by nonlinearly integrated equations. Finding specific solutions to such equations plays an important role in studying the dynamics of phenomena occurring in various scientific and engineering fields, such as solid state physics, fluid mechanics, plasma physics and nonlinear optics. There are several methods for obtaining real and soliton, soliton-like solutions of such equations: the inverse scattering method, the Hirota’s bilinear method, Darboux transformation methods, the tanh-coth and the sine-cosine methods. In our work, we studied the two-dimensional Hirota equation, which is a modified nonlinear Schrödinger equation. The nonlinear Hirota equation is one of the integrating equations and the Hirota system is used in the field of study of optical fiber systems, physics, telecommunications and other engineering fields to describe many nonlinear phenomena. To date, the first, second, and n-order Darboux transformations have been developed for the two- dimensional system of Hirota equations, and the soliton, rogue wave solutions have been determined by various methods. In this article, we consider the two-dimensional nonlinear Hirota equations. Using the Lax pair and Darboux transformation we obtained the first and the second multi-line soliton solutions for this equation and provided graphical representation.

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18

El-Nabulsi, Rami Ahmad. "Nonlinear integro-differential Einstein’s field equations from nonstandard Lagrangians." Canadian Journal of Physics 92, no. 10 (October 2014): 1149–53. http://dx.doi.org/10.1139/cjp-2013-0713.

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Given a manifold [Formula: see text] described by coordinates {xμ} and a space–time metric gμν on [Formula: see text] describing the gravitational field whose standard action is the Einstein–Hilbert action, we observe that if the action functional of spinor fields {Ψ(S)(x)}, S = 1, 2, …, N representing the matter and gauge fields holds a nonstandard exponential Lagrangian, the modified Einstein field equations acquire nonlinear partial integro-differential forms where both spinor and gravitational fields come out together.

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19

Richter, E. W. "Similarity Solutions of the Force-free Magnetic Field Equations." Zeitschrift für Naturforschung A 49, no. 9 (September 1, 1994): 902–12. http://dx.doi.org/10.1515/zna-1994-0914.

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Abstract Force-free magnetic fields are described as solutions of special nonlinear partial differential equations which are replaced frequently through linear equations. To record the diversity of the structures of these fields, a discussion of the nonlinear equations is necessary. For this purpose the method of similarity analysis is used. The Lie symmetry groups admitted by the nonlinear equations for force-free magnetic fields are presented. To record and classify the different types of group-invariant solutions, one-and two-dimensional optimal systems of subalgebras are listed. The reduced equations of the two-dimensional optimal system are systems of ordinary differential equations, and their solutions define similarity solutions which are force-free magnetic fields. Only in one case is it necessary to calculate similarity solutions numerically. The corresponding reduced equations are a nonautonomous dynamical system with the similarity variable in the place of time.

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20

Mitra, Indranil, and Pranab Krishna Chanda. "A New Class of Exact Solutions to a Generalized form of Charap’s Nonlinear Chiral Field Equations of Field Theory." Annals of Pure and Applied Mathematics 14, no. 3 (October 17, 2017): 417–26. http://dx.doi.org/10.22457/apam.v14n3a8.

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21

Kuman, Maria. "Crystals Influence the Body through our Weak Nonlinear Electromagnetic Field (NEMF)." Journal of Natural & Ayurvedic Medicine 3, no. 3 (July 15, 2019): 1–2. http://dx.doi.org/10.23880/jonam-16000200.

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In article [1], we presented our measurements about the effect of crystals on the human health and wellbeing. In the present article, we are going to explain how this is done. In [2], we used nonlinear mathematical model to describe the effect of acupuncture treatment. Nonlinear equations have more than one solution and our nonlinear equation had two solutions-electric impulse and wave. Electric impulses generated at acupuncture treatment and propagating along the acupuncture meridian were already measured in China. However, nobody has measured waves generated at acupuncture treatment and propagating along the acupuncture meridian.

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22

Clop, Albert, and Banhirup Sengupta. "Nonlinear transport equations and quasiconformal maps." Annales Fennici Mathematici 48, no. 1 (May 16, 2023): 375–87. http://dx.doi.org/10.54330/afm.130026.

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We prove existence of solutions to a nonlinear transport equation in the plane, for which the velocity field is obtained as the convolution of the classical Cauchy kernel with the unknown. Even though the initial datum is bounded and compactly supported, the velocity field may have unbounded divergence. The proof is based on the compactness property of quasiconformal mappings.

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23

Kruglikov, Boris. "Involutivity of field equations." Journal of Mathematical Physics 51, no. 3 (2010): 032502. http://dx.doi.org/10.1063/1.3305321.

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24

Byeon, Jaeyoung, Ohsang Kwon, and Jinmyoung Seok. "Nonlinear scalar field equations involving the fractional Laplacian." Nonlinearity 30, no. 4 (March 15, 2017): 1659–81. http://dx.doi.org/10.1088/1361-6544/aa60b4.

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25

Jeanjean, Louis, and Sheng-Sen Lu. "Nonradial normalized solutions for nonlinear scalar field equations." Nonlinearity 32, no. 12 (November 4, 2019): 4942–66. http://dx.doi.org/10.1088/1361-6544/ab435e.

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26

Mohammadi, M., and N. Riazi. "Approaching Integrability in Bi-Dimensional Nonlinear Field Equations." Progress of Theoretical Physics 126, no. 2 (August 1, 2011): 237–48. http://dx.doi.org/10.1143/ptp.126.237.

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27

Yu, Rotha P., David M. Paganin, and Michael J. Morgan. "Inferring nonlinear parabolic field equations from modulus data." Physics Letters A 341, no. 1-4 (June 2005): 156–63. http://dx.doi.org/10.1016/j.physleta.2005.04.065.

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28

Leo, R. A., and G. Soliani. "Incomplete Lie algebras generating integrable nonlinear field equations." Physics Letters B 222, no. 3-4 (May 1989): 415–18. http://dx.doi.org/10.1016/0370-2693(89)90335-3.

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29

Alfinito, E., M. Leo, R. A. Leo, M. Palese, and G. Soliani. "Integrable nonlinear field equations and loop algebra structures." Physics Letters B 352, no. 3-4 (June 1995): 314–20. http://dx.doi.org/10.1016/0370-2693(95)00561-x.

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30

Molle, Riccardo, and Donato Passaseo. "Multiplicity of solutions of nonlinear scalar field equations." Rendiconti Lincei - Matematica e Applicazioni 26, no. 1 (2015): 75–82. http://dx.doi.org/10.4171/rlm/693.

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31

Pomeau, Y. "Asymptotic time behaviour of nonlinear classical field equations." Nonlinearity 5, no. 3 (May 1, 1992): 707–20. http://dx.doi.org/10.1088/0951-7715/5/3/005.

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32

Gürses, Metin. "Integrability of Three Dimensional Gravity Field Equations." Journal of Physics: Conference Series 2191, no. 1 (February 1, 2022): 012013. http://dx.doi.org/10.1088/1742-6596/2191/1/012013.

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Abstract We show that the tree dimensional Einstein vacuum feld equations with cosmological constant are integrable. Using the sl(2, R) valued soliton connections we obtain the metric of the spacetime in terms of the dynamical variables of the integrable nonlinear partial diferential equations.

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33

LI, HE, XIANG-HUA MENG, and BO TIAN. "BILINEAR FORM AND SOLITON SOLUTIONS FOR THE COUPLED NONLINEAR KLEIN–GORDON EQUATIONS." International Journal of Modern Physics B 26, no. 15 (June 5, 2012): 1250057. http://dx.doi.org/10.1142/s0217979212500579.

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With the coupling of a scalar field, a generalization of the nonlinear Klein–Gordon equation which arises in the relativistic quantum mechanics and field theory, i.e., the coupled nonlinear Klein–Gordon equations, is investigated via the Hirota method. With the truncated Painlevé expansion at the constant level term with two singular manifolds, the coupled nonlinear Klein–Gordon equations are transformed to a bilinear form. Starting from the bilinear form, with symbolic computation, we obtain the N-soliton solutions for the coupled nonlinear Klein–Gordon equations.

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34

Cao, Dong Bo, and Jia Ren Yan. "Traveling Wave Exact Solutions for Nonlinear Coupled Scalar Field Equations." Advanced Materials Research 284-286 (July 2011): 2053–56. http://dx.doi.org/10.4028/www.scientific.net/amr.284-286.2053.

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In the present paper, with the aid of symbolic computation, the nonlinear coupled scalar field equations relevant to materials physics are investigated by using the trigonometric function transform method. More exact traveling wave solutions are obtained for nonlinear coupled scalar field equations. The solutions obtained in this paper include four kinds of soliton solutions and four kinds of trigonometric function solutions.

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35

Courvoisier, A., D. W. Hughes, and M. R. E. Proctor. "Self-consistent mean-field magnetohydrodynamics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2114 (October 29, 2009): 583–601. http://dx.doi.org/10.1098/rspa.2009.0384.

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We consider the linear stability of two-dimensional nonlinear magnetohydrodynamic basic states to long-wavelength three-dimensional perturbations. Following Hughes & Proctor (Hughes & Proctor 2009 Proc. R. Soc. A 465 , 1599–1616 ( doi:10.1098/rspa.2008.0493 )), the two-dimensional basic states are obtained from a specific forcing function in the presence of an initially uniform mean field of strength . By extending to the nonlinear regime the kinematic analysis of Roberts (Roberts 1970 Phil. Trans. R. Soc. Lond. A 266 , 535–558 ( doi:10.1098/rsta.1970.0011 )), we show that it is possible to predict the growth rate of these perturbations by applying mean-field theory to both the momentum and the induction equations. If , these equations decouple and large-scale magnetic and velocity perturbations may grow via the kinematic α -effect and the anisotropic kinetic alpha instability, respectively. However, if , the momentum and induction equations are coupled by the Lorentz force; in this case, we show that four transport tensors are now necessary to determine the growth rate of the perturbations. We illustrate these situations by numerical examples; in particular, we show that a mean-field description of the nonlinear regime based solely on a quenched α coefficient is incorrect.

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36

Caponigro, Marco, Benedetto Piccoli, Francesco Rossi, and Emmanuel Trélat. "Mean-field sparse Jurdjevic–Quinn control." Mathematical Models and Methods in Applied Sciences 27, no. 07 (April 11, 2017): 1223–53. http://dx.doi.org/10.1142/s0218202517400140.

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We consider nonlinear transport equations with non-local velocity describing the time-evolution of a measure. Such equations often appear when considering the mean-field limit of finite-dimensional systems modeling collective dynamics. We address the problem of controlling these equations by means of a time-varying bounded control action localized on a time-varying control subset of small Lebesgue measure. We first define dissipativity for nonlinear transport equations in terms of Lie derivatives of a Lyapunov function depending on the measure. Then, assuming that the uncontrolled system is dissipative, we provide an explicit construction of a control law steering the system to an invariant sublevel of the Lyapunov function. The control function and the control domain are designed in terms of the Lie derivatives of the Lyapunov function. In this sense the construction can be seen as an infinite-dimensional analogue of the well-known Jurdjevic–Quinn procedure. Moreover, the control law presents sparsity properties in the sense that the support of the control is small. Finally, we show that our result applies to a large class of kinetic equations modeling multi-agent dynamics.

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37

Açık, Özgür. "Field equations from Killing spinors." Journal of Mathematical Physics 59, no. 2 (February 2018): 023501. http://dx.doi.org/10.1063/1.4989434.

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38

FAN EN-GUI, ZHANG HONG-QING, and LIN GANG. "EXACT SOLUTIONS TO THE NONLINEAR COUPLED SCALAR FIELD EQUATIONS." Acta Physica Sinica 47, no. 7 (1998): 1064. http://dx.doi.org/10.7498/aps.47.1064.

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39

NISSIMOV, E., S. PACHEVA, and S. SOLOMON. "ACTION PRINCIPLE FOR OVERDETERMINED SYSTEMS OF NONLINEAR FIELD EQUATIONS." International Journal of Modern Physics A 04, no. 03 (February 1989): 737–52. http://dx.doi.org/10.1142/s0217751x89000352.

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We propose a general scheme for constructing an action principle for arbitrary consistent overdetermined systems of nonlinear field equations. The principal tool is the BFV-BRST formalism. There is no need for star-product nor Chern-Simons forms. The main application of this general construction is the derivation of a superspace action in terms of unconstrained superfields for the D = 10N = 1 Super-Yang-Mills theory. The latter contains cubic as well as quartic interactions.

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40

Khrennikov, Andrei. "Nonlinear Schrödinger equations from prequantum classical statistical field theory." Physics Letters A 357, no. 3 (September 2006): 171–76. http://dx.doi.org/10.1016/j.physleta.2006.04.046.

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41

Vernov, S. Yu. "Exact solutions of nonlocal nonlinear field equations in cosmology." Theoretical and Mathematical Physics 166, no. 3 (March 2011): 392–402. http://dx.doi.org/10.1007/s11232-011-0031-0.

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42

Malec, Edward. "The absence of small solutions of nonlinear field equations." Journal of Mathematical Physics 29, no. 1 (January 1988): 235–37. http://dx.doi.org/10.1063/1.528179.

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43

Ziepke, Alexander, Steffen Martens, and Harald Engel. "Control of Nonlinear Wave Solutions to Neural Field Equations." SIAM Journal on Applied Dynamical Systems 18, no. 2 (January 2019): 1015–36. http://dx.doi.org/10.1137/18m1197278.

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44

Ikoma, Norihisa. "On radial solutions of inhomogeneous nonlinear scalar field equations." Journal of Mathematical Analysis and Applications 386, no. 2 (February 2012): 744–62. http://dx.doi.org/10.1016/j.jmaa.2011.08.032.

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45

Steeb, Willi-Hans, Yorick Hardy, and Ruedi Stoop. "Bessel Functions, Recursion and a Nonlinear Field Equation." Zeitschrift für Naturforschung A 56, no. 9-10 (October 1, 2001): 710–12. http://dx.doi.org/10.1515/zna-2001-0919.

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46

Wennekers, Thomas. "Dynamic Approximation of Spatiotemporal Receptive Fields in Nonlinear Neural Field Models." Neural Computation 14, no. 8 (August 1, 2002): 1801–25. http://dx.doi.org/10.1162/089976602760128027.

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This article presents an approximation method to reduce the spatiotemporal behavior of localized activation peaks (also called “bumps”) in nonlinear neural field equations to a set of coupled ordinary differential equations (ODEs) for only the amplitudes and tuning widths of these peaks. This enables a simplified analysis of steady-state receptive fields and their stability, as well as spatiotemporal point spread functions and dynamic tuning properties. A lowest-order approximation for peak amplitudes alone shows that much of the well-studied behavior of small neural systems (e.g., the Wilson-Cowan oscillator) should carry over to localized solutions in neural fields. Full spatiotemporal response profiles can further be reconstructed from this low-dimensional approximation. The method is applied to two standard neural field models: a one-layer model with difference-of-gaussians connectivity kernel and a two-layer excitatory-inhibitory network. Similar models have been previously employed in numerical studies addressing orientation tuning of cortical simple cells. Explicit formulas for tuning properties, instabilities, and oscillation frequencies are given, and exemplary spatiotemporal response functions, reconstructed from the low-dimensional approximation, are compared with full network simulations.

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47

Tuszyński, J. A., and J. M. Dixon. "A Derivation of Relativistically-Invariant Nonlinear Field Equations for Strongly Interacting Many-Body Systems." International Journal of Modern Physics B 11, no. 07 (March 20, 1997): 929–44. http://dx.doi.org/10.1142/s0217979297000484.

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We re-examine the derivation of nonlinear field equations for a system of strongly interacting quasiparticles. Emphasis is placed on typical dispersion relations in the relativistic regime. Through Heisenberg's equations of motion for second-quantised operators we demonstrate that interacting many-body systems are described by a nonlinear Klein–Gordon type field equation. Its nonrelativistic equivalent was previously shown to be of the nonlinear Schrödinger type.

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48

Gómez‐Treviño, E. "Nonlinear integral equations for electromagnetic inverse problems." GEOPHYSICS 52, no. 9 (September 1987): 1297–302. http://dx.doi.org/10.1190/1.1442390.

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The scaling properties of Maxwell’s equations allow the existence of simple yet general nonlinear integral equations for electrical conductivity. These equations were developed in an attempt to reduce the generality of linearization to the exclusive scope of electromagnetic problems. The reduction is achieved when the principle of similitude for quasi‐static fields is imposed on linearized forms of the field equations. The combination leads to exact integral relations which represent a unifying framework for the general electromagnetic inverse problem. The equations are of the same form in both time and frequency domains and hold for all observations that scale as electric and magnetic fields do; direct current resistivity and magnetometric resistivity methods are considered as special cases. The kernel functions of the integral equations are closely related, through a normalization factor, to the Frechét kernels of the conventional equations obtained by linearization. Accordingly, the sensitivity functions play the role of weighting functions for electrical conductivity despite the nonlinear dependence of the model and the data. In terms of the integral equations, the inverse problem consists of extracting information about a distribution of conductivity from a given set of its spatial averages. The form of the new equations leads to the consideration of their numerical solution through an approximate knowledge of their kernel functions. The integral equation for magnetotelluric soundings illustrates this approach in a simple fashion.

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49

ROTA NODARI, SIMONA. "THE RELATIVISTIC MEAN-FIELD EQUATIONS OF THE ATOMIC NUCLEUS." Reviews in Mathematical Physics 24, no. 04 (May 2012): 1250008. http://dx.doi.org/10.1142/s0129055x12500080.

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In nuclear physics, the relativistic mean-field theory describes the nucleus as a system of Dirac nucleons which interact via meson fields. In a static case and without nonlinear self-coupling of the σ meson, the relativistic mean-field equations become a system of Dirac equations where the potential is given by the meson and photon fields. The aim of this work is to prove the existence of solutions of these equations. We consider a minimization problem with constraints that involve negative spectral projectors and we apply the concentration-compactness lemma to find a minimizer of this problem. We show that this minimizer is a solution of the relativistic mean-field equations considered.

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50

Dost, S., and P. G. Glockner. "On Beltrami-Michell-Like Equations for Nonlinear Elastic Dielectrics." Transactions of the Canadian Society for Mechanical Engineering 10, no. 3 (September 1986): 167–73. http://dx.doi.org/10.1139/tcsme-1986-0019.

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Beltrami-Michell-like equations for nonlinear elastic dielectrics are obtained by choosing the deformation gradient, the polarization gradient and the polarization vector as independent field variables, so as to yield linear compatibility equations. The corresponding stress field also yields linear balance equations. Two simple examples for the case of semilinear isotropic elastic dielectrics are solved to illustrate the theory.

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