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Journal articles on the topic 'Nonlinear field equations'

Author: Grafiati

Published: 18 May 2024

Last updated: 31 July 2025

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1

Tan, Jinggang, Ying Wang, and Jianfu Yang. "Nonlinear fractional field equations." Nonlinear Analysis: Theory, Methods & Applications 75, no. 4 (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 (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 (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 (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 (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 (1985): 26–32. http://dx.doi.org/10.1007/bf03024171.

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7

Bekova, G. T., and A. A. Zhadyranova. "MULTI-LINE SOLITON SOLUTIONS FOR THE TWO-DIMENSIONAL NONLINEAR HIROTA EQUATION." PHYSICO-MATHEMATICAL SERIES 2, no. 336 (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 so

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8

Bruce, S. A. "Nonlinear Maxwell equations and strong-field electrodynamics." Physica Scripta 97, no. 3 (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 counter

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9

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

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10

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

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11

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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12

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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13

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

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14

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

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15

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

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16

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

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17

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

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18

Richter, E. W. "Similarity Solutions of the Force-free Magnetic Field Equations." Zeitschrift für Naturforschung A 49, no. 9 (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 reduce

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19

El-Nabulsi, Rami Ahmad. "Nonlinear integro-differential Einstein’s field equations from nonstandard Lagrangians." Canadian Journal of Physics 92, no. 10 (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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20

Kuman, Maria. "Crystals Influence the Body through our Weak Nonlinear Electromagnetic Field (NEMF)." Journal of Natural & Ayurvedic Medicine 3, no. 3 (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 prop

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21

Clop, Albert, and Banhirup Sengupta. "Nonlinear transport equations and quasiconformal maps." Annales Fennici Mathematici 48, no. 1 (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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22

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

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23

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

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24

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

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25

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 (2005): 156–63. http://dx.doi.org/10.1016/j.physleta.2005.04.065.

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26

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

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27

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 (1995): 314–20. http://dx.doi.org/10.1016/0370-2693(95)00561-x.

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28

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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29

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

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30

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 (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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31

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 (2017): 417–26. http://dx.doi.org/10.22457/apam.v14n3a8.

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32

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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33

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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34

Gürses, Metin. "Integrability of Three Dimensional Gravity Field Equations." Journal of Physics: Conference Series 2191, no. 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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35

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 (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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36

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 (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 possib

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37

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 (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 di

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38

Gómez‐Treviño, E. "Nonlinear integral equations for electromagnetic inverse problems." GEOPHYSICS 52, no. 9 (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 bot

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39

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

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40

ROTA NODARI, SIMONA. "THE RELATIVISTIC MEAN-FIELD EQUATIONS OF THE ATOMIC NUCLEUS." Reviews in Mathematical Physics 24, no. 04 (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 proble

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41

Wennekers, Thomas. "Dynamic Approximation of Spatiotemporal Receptive Fields in Nonlinear Neural Field Models." Neural Computation 14, no. 8 (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-

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42

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 (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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43

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

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44

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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45

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 (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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46

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

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47

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

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48

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

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49

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 (2019): 1015–36. http://dx.doi.org/10.1137/18m1197278.

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50

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

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