Traveling wave solutions for the mKdV equation and the Gardner equations by new approach of the generalized \((G'/G)\)-expansion method

DOI10.1016/j.joems.2014.01.001zbMath1304.35180OpenAlexW2085253981MaRDI QIDQ467065

M. Ali Akbar, Md. Nur Alam

Publication date: 3 November 2014

Published in: Journal of the Egyptian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.joems.2014.01.001

zbMATH Keywords

hyperbolic functionstrigonometric functionsrational functionsexact solutionstraveling wave solutionssolitary wave solutionsGardner equationmKdV equationnew generalized \((G'/G)\)-expansion method

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Wave equation (35L05) Traveling wave solutions (35C07) Soliton solutions (35C08)

Related Items

Application of the novel \((G'/G)\)-expansion method to the regularized long wave equation ⋮ New exact solutions for Kudryashov-Sinelshchikov equation

Cites Work

• Traveling wave solutions of the nonlinear Drinfel'd-Sokolov-Wilson equation and modified Benjamin-Bona-Mahony equations
• The \((\frac{G'}{G})\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
• A generalized \((\frac{G'}{G})\)-expansion method for the mKdV equation with variable coefficients
• Application of the \((\frac{G'}{G})\)-expansion method for nonlinear evolution equations
• Modified simple equation method for nonlinear evolution equations
• Exp-function method for nonlinear wave equations
• Application of the Cole-Hopf transformation for finding exact solutions to several forms of the seventh-order KdV equation
• Compactons dispersive structures for variants of the \(K(n,n)\) and the KP equations
• Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic function solutions to \((1+1)\)-dimensional dispersive long wave equation
• A generalized and improved \((G'/G)\)-expansion method for nonlinear evolution equations
• New solitons and kink solutions for the Gardner equation
• Exact solutions of coupled nonlinear evolution equations
• Exact solutions of compact and noncompact structures for the KP-BBM equation
• Explicit solutions to three nonlinear physical models
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