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Extend three-wave method for the \((1+2)\)-dimensional Itô equation. (English) Zbl 1200.35280

Summary: The extend three-wave method (ETM) is used to construct the novel multi-wave solutions of the \((1+2)\)-dimensional Ito equation. As a result, three-soliton solution, doubly periodic solitary wave solutions, periodic two solitary wave solutions are obtained. It is shown that the Extend three-wave method may provide us with a straightforward and effective mathematical tool for seeking multi-wave solutions of higher dimensional nonlinear evolution equations.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
35B10 Periodic solutions to PDEs
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