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Exact solutions of the coupled KdV system via a formally variable separation approach. (English) Zbl 1164.81306

Summary: Most of the nonlinear physics systems are essentially nonintegrable. There is no very good analytical approach to solve nonintegrable systems. The variable separation approach is a powerful method in linear physics. In this letter, the formal variable separation approach is established to solve the generalized nonlinear mathematical physics equation. The method is valid not only for integrable models but also for nonintegrable models. Taking a nonintegrable coupled KdV equation system as a simple example, abundant solitary wave solutions and conoid wave solutions are revealed.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q40 PDEs in connection with quantum mechanics
35Q53 KdV equations (Korteweg-de Vries equations)
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