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Various kinds waves and solitons interaction solutions of Boussinesq equation describing ultrashort pulse in quadratic nonlinear medium. (English) Zbl 1365.35152

Summary: The consistent tanh expansion (CTE) method is applied to the \((2+1)\)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution, and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlevé truncated expansion method. And we investigate interactive properties of solitons and periodic waves.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35C08 Soliton solutions
35C10 Series solutions to PDEs
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