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New variable separation solutions and nonlinear phenomena for the \((2+1)\)-dimensional modified Korteweg-de Vries equation. (English) Zbl 1221.35351

Summary: Variable separation approach, which is a powerful approach in the linear science, has been successfully generalized to the nonlinear science as nonlinear variable separation methods. The \((2 + 1)\)-dimensional modified Korteweg-de Vries (mKdV) equation is hereby investigated, and new variable separation solutions are obtained by the truncated Painlevé expansion method and the extended tanh-function method. By choosing appropriate functions for the solution involving three low-dimensional arbitrary functions, which is derived by the truncated Painlevé expansion method, two kinds of nonlinear phenomena, namely, dromion reconstruction and soliton fission phenomena, are discussed.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
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