The improved \((\frac{G^{\prime}}{G})\)-expansion method and its applications to the Broer-Kaup equations and approximate long water wave equations

DOI10.1016/J.AMC.2010.03.026zbMath1311.76013OpenAlexW1997386549MaRDI QIDQ979288

Chenxia Zhao, Shimin Guo, Yu-Bin Zhou

Publication date: 25 June 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2010.03.026

zbMATH Keywords

nonlinear evolution equationsolitary wave solutionhyperbolic function

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Solitary waves for incompressible inviscid fluids (76B25) Soliton equations (35Q51)

Related Items (6)

Exact solutions to the Sharma-Tasso-Olver equation by using improved \(G'/G\)-expansion method ⋮ New Jacobi elliptic function solutions for the Zakharov equations ⋮ The extended multiple \(\left(G'/ G\right)\)-expansion method and its application to the Caudrey-Dodd-Gibbon equation ⋮ New exact solutions for a higher order wave equation of KdV type using multiple \(G^\prime / G\)-expansion methods ⋮ The compound \(\left(\frac{G'}{G}\right)\)-expansion method and double non-traveling wave solutions of \((2+1)\)-dimensional nonlinear partial differential equations ⋮ Exact solutions of nonlinear wave equations using \((G^\prime/G, 1/G)\)-expansion method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The \((\frac{G'}{G})\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
• Sub-ODE method and solitary wave solutions for higher order nonlinear Schrödinger equation
• Auxiliary equation method for the mKdV equation with variable coefficients
• A generalized \((\frac{G'}{G})\)-expansion method for the mKdV equation with variable coefficients
• The sine-cosine method for obtaining solutions with compact and noncompact structures
• Periodic structures based on variable separation solution of the (2+1)-dimensional boiti-leon-pempinelli equation
• The extended \(\left( \frac {G^{\prime}}{G}\right)\)-expansion method and its applications to the Whitham-Broer-Kaup-like equations and coupled Hirota-Satsuma KdV equations
• The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations
• The extended tanh method for abundant solitary wave solutions of nonlinear wave equations
• A further improved extended Fan sub-equation method for \((2+1)\)-dimensional breaking soliton equations
• The novel solutions of auxiliary equation and their application to the \((2 + 1)\)-dimensional Burgers equations
• Symbolic computation and non-travelling wave solutions of \((2 + 1)\)-dimensional nonlinear evolution equations
• Semifoldons with Fusion and fission properties of \((2 + 1)\)-dimensional nonlinear system
• Bäcklund transformations and their applications
• Similarity reductions from extended Painlevé expansions for nonintegrable evolution equations
• The periodic wave solutions for the Klein-Gordon-Schrödinger equations
• Complexiton solutions to the Korteweg-de Vries equation
• Periodic wave solutions to a coupled KdV equations with variable coefficients
• Solitary wave solutions for variant Boussinesq equations
• Exact solutions for a compound KdV-Burgers equation
• The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations
• Application of the \(\frac{G^\prime}{G}\)-expansion to travelling wave solutions of the Broer-Kaup and the approximate long water wave equations
• The periodic wave solutions and solitary wave solutions for a class of nonlinear partial differential equations
• 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
• Various exact solutions of nonlinear Schrödinger equation with two nonlinear terms
• The sine-cosine and the tanh methods: reliable tools for analytic treatment of nonlinear dispersive equations
• Multiple kink solutions and multiple singular kink solutions for the (2 + 1)-dimensional Burgers equations
• A Higher-Order Water-Wave Equation and the Method for Solving It
• Approximate equations for long water waves
• Application of ModifiedG′/G-Expansion Method to Traveling Wave Solutions for Whitham–Broer–Kaup-Like Equations
• Variational methods and applications to water waves

This page was built for publication: The improved \((\frac{G^{\prime}}{G})\)-expansion method and its applications to the Broer-Kaup equations and approximate long water wave equations