Travelling wave solutions of some classes of nonlinear evolution equations in \((1+1)\) and higher dimensions.

DOI10.1016/j.matcom.2003.09.024zbMath1039.65071OpenAlexW2039758268MaRDI QIDQ1427728

D. Massart

Publication date: 14 March 2004

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2003.09.024

zbMATH Keywords

stabilitysolitary waveswave equationsnonlinear evolution equationstraveling wave solutionsKorteweg-de Vries equationstanh methodLiouville's equationtanh series solution method

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) KdV equations (Korteweg-de Vries equations) (35Q53) Second-order nonlinear hyperbolic equations (35L70) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (11)

Numerical solutions of some nonlinear evolution equations by Chebyshev spectral collocation methods ⋮ Solutions of the Cahn-Hilliard equation ⋮ Numerical solutions for some coupled nonlinear evolution equations by using spectral collocation method ⋮ Numerical solutions of the generalized kuramoto-sivashinsky equation using B-spline functions ⋮ Surfaces of a constant negative curvature ⋮ Traveling wave solutions using the variational method and the tanh method for nonlinear coupled equations ⋮ A Chebyshev spectral collocation method for solving Burgers'-type equations ⋮ Construction of solitary wave solutions for variants of theK(n, n) equation ⋮ Conservation laws and exact solutions for some nonlinear partial differential equations ⋮ Numerical solutions of the generalized Kuramoto-Sivashinsky equation by Chebyshev spectral collocation methods ⋮ Cnoidal wave solutions for a class of fifth-order KdV equations

Cites Work

• Unnamed Item
• Symbolic methods to construct exact solutions of nonlinear partial differential equations
• Travelling-wave solutions of coupled nonlinear evolution equations
• Parametric envelope solitons in coupled Korteweg-de Vries equations
• Solitary wave solutions of nonlinear wave equations
• Exact solutions for some coupled nonlinear equations. II
• Series solution of nonlinear coupled reaction-diffusion equations
• New special solutions of the `Brusselator' reaction model
• Approximate solution of the damped Burgers equation
• The tanh method: II. Perturbation technique for conservative systems
• The tanh method: I. Exact solutions of nonlinear evolution and wave equations

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