New generalized method to construct new non-travelling wave solutions and travelling wave solutions of K–D equations

DOI10.1080/00207160701504121zbMath1149.65086OpenAlexW2018103125MaRDI QIDQ3526052

Dahai Zhang, Fang Chen, Hong-Qing Zhang, Yu-Jie Ren

Publication date: 24 September 2008

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160701504121

zbMATH Keywords

non-travelling wave solution\((2+1)\)-dimensional K-D equationgeneralized algebra methodKonopelchenko-Dubrovsky (K-D) equation

Mathematics Subject Classification ID

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

Cites Work

• A direct approach with computerized symbolic computation for finding a series of traveling waves to nonlinear equations
• A generalized F-expansion method to find abundant families of Jacobi elliptic function solutions of the \((2+1)\)-dimensional Nizhnik-Novikov-Veselov equation
• Exact solutions to the double sinh-Gordon equation by the tanh method and a variable separated ODE method
• New generalized hyperbolic functions and auto-Bäcklund transformation to find new exact solutions of the \((2+1)\)-dimensional NNV equation
• A Chebyshev spectral method for solving Korteweg-de Vries equation with hydrodynamical application
• Symbolic computation and new families of exact soliton-like solutions of Konopelchenko-Dubrov\-sky equations
• An improved algebra method and its applications in nonlinear wave equations
• A new generalized algebra method and its application in the \((2+1)\)-dimensional Boiti-Leon-Pempinelli equation