Automatic computation of the travelling wave solutions to nonlinear PDEs

DOI10.1016/j.cpc.2007.12.004zbMath1196.35010OpenAlexW2045598763MaRDI QIDQ710262

Songxin Liang, David J. Jeffrey

Publication date: 18 October 2010

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2007.12.004

zbMATH Keywords

exact solutionsymbolic computationnonlinear partial differential equationtravelling wave solutiontanh-function method\texttt{TWS}

Mathematics Subject Classification ID

Nonnumerical algorithms (68W05) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Software, source code, etc. for problems pertaining to partial differential equations (35-04)

Related Items (3)

Sufficient conditions for the preservation of the boundedness in a numerical method for a physical model with transport memory and nonlinear damping ⋮ A new algorithm for automatic computation of solitary wave solutions to nonlinear partial differential equations based on the Exp-function method ⋮ On nonlinear differential equation with exact solutions having various pole orders

Uses Software

• Maple
• RAEEM
• RATH
• MACSYMA
• PDEtools
• PDESpecialSolutions

Cites Work

• Unnamed Item
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• An automated \(\tanh\)-function method for finding solitary wave solutions to nonlinear evolution equations
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• Modified extended tanh-function method and its applications to nonlinear equations
• Travelling solitary wave solutions to a seventh-order generalized KdV equation
• Travelling solitary wave solutions to a compound KdV-Burgers equation.
• Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs
• Extended tanh-function method and its applications to nonlinear equations
• Solitary wave solutions of nonlinear wave equations
• A family of exact travelling wave solutions to nonlinear evolution and wave equations
• The tanh method: I. Exact solutions of nonlinear evolution and wave equations
• Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA
• Modified extended tanh-function method for solving nonlinear partial differential equations

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