The homogeneous balance method and its application to the Benjamin-Bona-Mahoney (BBM) equation

DOI10.1016/j.amc.2009.05.027zbMath1202.35209OpenAlexW2055317498MaRDI QIDQ609268

Mohammed Khalfallah, A. S. Abdel Rady, El-Sayed Osman

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.2009.05.027

zbMATH Keywords

Riccati equationsoliton solutionstraveling wave solutionshomogeneous balance methodBenjamin-Bona-Mahoney equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Software, source code, etc. for problems pertaining to partial differential equations (35-04) Traveling wave solutions (35C07) Soliton solutions (35C08) Methods of ordinary differential equations applied to PDEs (35A24)

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Cites Work

• Adiabatic parameter dynamics of perturbed solitary waves
• New exact traveling wave solutions of the \((3 + 1)\) dimensional Kadomtsev-Petviashvili (KP) equation
• Soliton perturbation theory for the generalized Benjamin-Bona-Mahoney equation
• Generalized extended tanh-function method and its application
• Numerical solitons of generalized Korteweg-de Vries equations
• The generalizing Riccati equation mapping method in non-linear evolution equation: Application to \((2 + 1)\)-dimensional Boiti-Leon-Pempinelle equation
• New periodic wave and soliton solutions for system of coupled Korteweg-de Vries equations
• A new note on a homogeneous balance method
• Two new applications of the homogeneous balance method
• Solitary wave solutions for variant Boussinesq equations
• New exact solutions to a solutions to a system of coupled KdV equations
• Exact traveling wave solutions of the Boussinesq-Burgers equation
• A note on the homogeneous balance method
• Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics
• Soliton solutions for a generalized Hirota-Satsuma coupled KdV equation and a coupled MKdV equation
• A new Bäcklund transformation and multi-soliton solutions to the KdV equation with general variable coefficients
• Auto-Bäcklund transformation and similarity reductions for general variable coefficient KdV equations

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