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The exact solutions to the generalized (2+1)-dimensional nonlinear wave equation
Results in PhysicsDue to the importance of the nonlinear partial differential equations in applied physics and engineering, many mathematicians and physicists are interesting to the nonlinear partial differential equations.
Jianping Li, Can Xu, Junliang Lu
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Exact Solutions to the Sharma-Tasso-Olver Equation by Using Improved G′/G-Expansion Method
Journal of Applied Mathematics, 2013 This paper is concerned with a double nonlinear dispersive equation: the Sharma-Tasso-Olver equation. We propose an improved G′/G-expansion method which is employed to investigate the solitary and periodic traveling waves of this equation.
Yinghui He, Shaolin Li, Yao Long
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The numerical solution of the nonlinear hyperbolic-parabolic heat equation
Discrete and Continuous Models and Applied Computational ScienceThe article discusses a mathematical model and a finite-difference scheme for the heating process of an infinite plate. The disadvantages of using the classical parabolic heat equation for this case and the rationale for using the hyperbolic heat ...
Vladislav N. Khankhasaev +1 more
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Study on Optimal Conventional Triaxial Strength Criterion of Rock Based on Gauss-Newton Method [PDF]
E3S Web of ConferencesConventional triaxial strength criteria are used widely to judge the rock failure states. In this paper, the nonlinear least squares method (Guass-newton method) is used to fit the regression relationships between the maximum principal stress σ1 as well ...
Tian Mengtao +4 more
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Solvability of Nonlinear Wave Equation with Nonlinear Integral Neumann Conditions
International Journal of Analysis and Applications, 2023 In this paper, we examine a nonlinear hyperbolic equation with a nonlinear integral condition. In particular, we prove the existence and the uniqueness of the linear problem by the Fadeo Galerkin method, and by applying an iterative process to some ...
Iqbal M. Batiha +5 more
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Riemann Invariants and Rank-k Solutions of Hyperbolic Systems [PDF]
, 2006 In this paper we employ a "direct method" in order to obtain rank-k solutions of any hyperbolic system of first order quasilinear differential equations in many dimensions.
Huard, Benoit, Grundland, A. Michel
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Nonlinear Engineering, 2023 In this study, a numerical approach is presented to solve the linear and nonlinear hyperbolic Volterra integrodifferential equations (HVIDEs). The regularization of a Legendre-collocation spectral method is applied for solving HVIDE of the second kind ...
Mirzaei G. F., Rostamy Davood
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Alexandria Engineering Journal, 2020 The present paper employs the space-time fractional nonlinear Bogoyavlenskii equation and Schrodinger equation. We perform a new method to take some new solitary wave phenomena for each equation.
Md Nur Alam, Cemil Tunç
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Results in Physics, 2023 In this paper, we study the extended (3+1)-dimensional nonlinear conformable Schrödinger equation with cubic–quintic nonlinearity. We use three different methods to obtain exact solutions of this equation: the G′/G expansion method, the extended ...
Mohammad Mirzazadeh +4 more
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A Hyperbolic Approximation of the Nonlinear Schrödinger Equation
Studies in Applied MathematicsABSTRACT We study a first‐order hyperbolic approximation of the nonlinear Schrödinger (NLS) equation. We show that the system is strictly hyperbolic and possesses a modified Hamiltonian structure, along with at least three conserved quantities that approximate those of NLS.
Abhijit Biswas +4 more
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