A new general algebraic method with symbolic computation and its application to two nonlinear differential equations with nonlinear terms of any order

DOI10.1016/j.amc.2006.05.018zbMath1107.65091OpenAlexW2060050041MaRDI QIDQ858797

Lina Song, Jing Wang, Xiao-Ling Zhang, Hong-Qing Zhang

Publication date: 11 January 2007

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2006.05.018

zbMATH Keywords

symbolic computationnonlinear evolution equationscompound KdV-Burgers equation with nonlinear terms of any ordergeneralized Riccati equation rational expansion methodsingle nonlinear reaction-diffusion equation with nonlinear terms of any order

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) KdV equations (Korteweg-de Vries equations) (35Q53) Reaction-diffusion equations (35K57) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items

A new improved Adomian decomposition method and its application to fractional differential equations ⋮ Some new and general solutions to the compound KdV-Burgers system with nonlinear terms of any order ⋮ New traveling wave solutions of Drinfel'd-Sokolov-Wilson equation using tanh and extended tanh methods

Uses Software

• Maple
• RATH

Cites Work

• RATH: A Maple package for finding travelling solitary wave solutions to nonlinear evolution equations
• Oscillatory instability of traveling waves for a KdV-Burgers equation
• Explicit exact solutions for compound KdV-type and compound KdV-Burgers-type equations with nonlinear terms of any order.
• Soliton like and multi-soliton like solutions for the Boiti-Leon-Pempinelli equation
• The tanh method, a simple transformation and exact analytical solutions for nonlinear reaction-diffusion equations
• On exact solutions of the nonlinear Schrödinger equations in optical fiber
• Travelling solitary wave solutions to a seventh-order generalized KdV equation
• A new Riccati equation rational expansion method and its application to \((2+1)\)-dimensional Burgers equation
• Wave Propagation in Nonlinear Lattice. II
• On Series Expansions Giving Closed-Form Solutions of Korteweg–de Vries-Like Equations
• The role of filters and the singular-value decomposition for the inverse Born approximation
• Modified extended tanh-function method for solving nonlinear partial differential equations
• Generalized hyperbolic-function method with computerized symbolic computation to construct the solitonic solutions to nonlinear equations of mathematical physics
• Explicit exact solitary-wave solutions for compound KdV-type and compound KdV-Burgers-type equations with nonlinear terms of any order

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