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Hamiltonian structure and new exact soliton solutions of some Korteweg–de Vries equations. (English) Zbl 1212.35414

Summary: In this paper, we discuss the Hamiltonian structure of Korteweg–de Vries equation, modified Korteweg–de Vries equation, and generalized Korteweg–de Vries equation. We proposed the Sine-function algorithm to obtain the exact solution for non-linear partial differential equations. This method is used to obtain the exact solutions for KdV, mKdV and GKdV equations. We also have applied the method to Burgers equation which does not admit Hamiltonian structure.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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