Multi soliton solution for the system of coupled Korteweg-de Vries equations

DOI10.1016/j.amc.2008.12.076zbMath1163.35467OpenAlexW1979423828MaRDI QIDQ1015796

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

Publication date: 30 April 2009

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

Full work available at URL: https://doi.org/10.1016/j.amc.2008.12.076

zbMATH Keywords

trigonometric functionBäcklund transformationLax pairsextended homogeneous balance method

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Soliton equations (35Q51) Geometric theory, characteristics, transformations in context of PDEs (35A30) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (13)

An effective approximation to the dispersive soliton solutions of the coupled KdV equation via combination of two efficient methods ⋮ Soliton solutions for some nonlinear partial differential equations in mathematical physics using He's variational method ⋮ Exact solitary wave solutions of the generalized \((2+1)\) dimensional Boussinesq equation ⋮ The Jacobi elliptic function method and its application for two component BKP hierarchy equations ⋮ New soliton solutions for a Kadomtsev-Petviashvili (KP) like equation coupled to a Schrödinger equation ⋮ Exact solution of a KdV equation with variable coefficients ⋮ A meshless based numerical technique for traveling solitary wave solution of Boussinesq equation ⋮ Variational approach, soliton solutions and singular solitons for new coupled ZK system ⋮ Explicit periodic solitary wave solutions for the \((2+1)\)-dimensional Boussinesq equation ⋮ Generalization of exp-function and other standard function methods ⋮ New periodic wave and soliton solutions for a Kadomtsev-Petviashvili (KP) like equation coupled to a Schrödinger equation ⋮ Derivation of soliton solutions to nonlinear evolution equations using He's variational principle ⋮ A mixed algorithm for numerical computation of soliton solutions of the coupled KdV equation: finite difference method and differential quadrature method

Uses Software

• JanetBasis

Cites Work

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• Two new applications of the homogeneous balance method
• Solitary wave solutions for variant Boussinesq equations
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• Exact traveling wave solutions of the Boussinesq-Burgers equation
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• Algorithmic method for deriving Lax pairs from the invariant Painlevé analysis of nonlinear partial differential equations
• Exact envelope-soliton solutions of a nonlinear wave equation
• Auto-Bäcklund transformation and similarity reductions for general variable coefficient KdV equations

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