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Exact M/W-shape solitary wave solutions determined by a singular traveling wave equation. (English) Zbl 1162.35341

Summary: It had been found that some nonlinear wave equations have the so-called “W/M”-shape-peaks solitons. What is the dynamical behavior of these solutions? To answer this question, all traveling wave solutions in the parameter space are investigated for a integrable water wave equation from a dynamical systems theoretical point of view. Exact explicit parametric representations of all solitary wave solutions are given.

MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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References:

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