A study on an integrable system of coupled KdV equations

DOI10.1016/j.cnsns.2009.11.031zbMath1222.37070OpenAlexW1978863798MaRDI QIDQ720196

Abdul-Majid Wazwaz

Publication date: 13 October 2011

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2009.11.031

zbMATH Keywords

resonanceHirota bilinear methodmultiple singular soliton solutionsmultiple-soliton solutionsKdV system

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)

Related Items (7)

Integrability and equivalence relationships of six integrable coupled Korteweg-de Vries equations ⋮ An effective approximation to the dispersive soliton solutions of the coupled KdV equation via combination of two efficient methods ⋮ Bäcklund transformation, superposition formulae and \(N\)-soliton solutions for the perturbed Korteweg-de Vries equation ⋮ On complete integrability for systems of differential equations ⋮ A note on ``A study on an integrable system of coupled KdV equations ⋮ Comment on ``A note on a study on an integrable system of coupled KdV equations ⋮ A mixed algorithm for numerical computation of soliton solutions of the coupled KdV equation: finite difference method and differential quadrature method

Uses Software

• MACSYMA
• HIROTA.MAX

Cites Work

• Symbolic methods to construct exact solutions of nonlinear partial differential equations
• The Hirota's direct method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Ito seventh-order equation
• Multiple-front solutions for the Burgers-Kadomtsev-Petviashvili equation
• Solitary wave solutions of the generalized shallow water wave (GSWW) equation by Hirota's method, tanh-coth method and exp-function method
• Multiple-soliton solutions for the Lax-Kadomtsev-Petviashvili (Lax-KP) equation
• The Hirota's direct method for multiple-soliton solutions for three model equations of shallow water waves
• Multiple-soliton solutions of two extended model equations for shallow water waves
• Multiple-soliton solutions for the Boussinesq equation
• Partial differential equations and solitary waves theory
• New solitons and kink solutions for the Gardner equation
• Single and multiple-soliton solutions for the \((2+1)\)-dimensional KdV equation
• Solitons and singular solitons for the Gardner-KP equation
• Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method
• Multiple-front solutions for the Burgers equation and the coupled Burgers equations
• Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics
• N-Soliton Solutions of Model Equations for Shallow Water Waves
• An Extension of Nonlinear Evolution Equations of the K-dV (mK-dV) Type to Higher Orders
• Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
• A New Form of Backlund Transformations and Its Relation to the Inverse Scattering Problem
• A search for bilinear equations passing Hirota’s three-soliton condition. I. KdV-type bilinear equations
• A search for bilinear equations passing Hirota’s three-soliton condition. II. mKdV-type bilinear equations
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