A sub-ODE method for generalized Gardner and BBM equation with nonlinear terms of any order

DOI10.1016/j.amc.2009.05.049zbMath1203.35236OpenAlexW2050097142MaRDI QIDQ609275

CuiLian Liu, Dianchen Lu

Publication date: 30 November 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2009.05.049

zbMATH Keywords

generalized BBM equationtraveling wave solutionssub-ODEgeneralized Gardner equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Traveling wave solutions (35C07) Methods of ordinary differential equations applied to PDEs (35A24)

Related Items (6)

\(M\)-truncated optical soliton and their characteristics to a nonlinear equation governing the certain instabilities of modulated wave trains ⋮ The extended Riccati equation mapping method for variable-coefficient diffusion-reaction and mKdV equations ⋮ The first integral method and some nonlinear models ⋮ New exact solutions for the generalized variable-coefficient Gardner equation with forcing term ⋮ Exact solutions for a generalized KdV-mkdv equation with variable coefficients ⋮ Traveling nonsmooth solution and conserved quantities of long nonlinear internal waves

Uses Software

• ATFM

Cites Work

• Elliptic solutions to a generalized BBM equation
• The improved sub-ODE method for a generalized KdV-mKdV equation with nonlinear terms of any order
• New exact solutions for the \((2 + 1)\)-dimensional generalized Broer-Kaup system
• Exp-function method for nonlinear wave equations
• An automated \(\tanh\)-function method for finding solitary wave solutions to nonlinear evolution equations
• Nonlinear variants of KdV and KP equations with compactons, solitons and periodic solutions
• Exact solutions for two nonlinear wave equations with nonlinear terms of any order
• New solitons and kink solutions for the Gardner equation
• Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method
• A sub-ODE method for finding exact solutions of a generalized KdV-mKdV equation with high-order nonlinear terms
• Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics
• ATFM

This page was built for publication: A sub-ODE method for generalized Gardner and BBM equation with nonlinear terms of any order