Travelling wave solutions of nonlinear evolution equations using the simplest equation method

DOI10.1016/j.camwa.2012.04.004zbMath1268.35107OpenAlexW2079494215MaRDI QIDQ356109

Chaudry Masood Khalique, Hossein Jafari, Nematollah Kadkhoda

Publication date: 25 July 2013

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2012.04.004

zbMATH Keywords

regularized long wave equationsolitary wave solutionssimplest equation methodparkes equationVakhnenko

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Traveling wave solutions (35C07)

Related Items (9)

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation ⋮ Propagation of traveling wave solutions to the Vakhnenko-Parkes dynamical equation via modified mathematical methods ⋮ Application of tan(φ(ξ)/2)-expansion method to burgers and foam drainage equations ⋮ Exact solutions of a KdV equation hierarchy with variable coefficients ⋮ Exact solutions of \(\phi^4\) equation using Lie symmetry approach along with the simplest equation and exp-function methods ⋮ Variable separation method for nonlinear time fractional biological population model ⋮ A novel analytical technique to obtain kink solutions for higher order nonlinear fractional evolution equations ⋮ Prandtl's boundary layer equation for two-dimensional flow: exact solutions via the simplest equation method ⋮ Application of the ITEM for solving three nonlinear evolution equations arising in fluid mechanics

Cites Work

• Application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations
• Application of (\(\frac{G'}{G}\))-expansion method to travelling wave solutions of three nonlinear evolution equation
• The sine-cosine method for obtaining solutions with compact and noncompact structures
• Exact solitary waves of the Fisher equation
• The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method.
• The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations
• The tanh and the sine-cosine methods for the complex modified KdV and the generalized KdV equations
• The \(\tan h\) method: solitons and periodic solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough equations
• Simplest equation method to look for exact solutions of nonlinear differential equations
• Extended tanh-function method and its applications to nonlinear equations
• New solitary wave solutions for the bad Boussinesq and good Boussinesq equations
• Painlevé Tests, Singularity Structure and Integrability
• The two loop soliton solution of the Vakhnenko equation
• Model equations for long waves in nonlinear dispersive systems

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