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Multi soliton solution for the system of coupled Korteweg-de Vries equations. (English) Zbl 1163.35467

Summary: We consider the system of coupled Korteweg-de Vries equations and establish the transformation which turns the coupled KdV equations into the single nonlinear partial differential equation, then we obtain an auto-Bäcklund transformation and Lax pairs by using the extended homogeneous balance method. Also, we obtain the multi soliton solutions and the new trigonometric function periodic solutions by using the generalized tanh method.

MSC:

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

Software:

JanetBasis
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References:

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