Peakon, cuspon, compacton, and loop solutions of a three-dimensional 3DKP\((3,2)\) equation with nonlinear dispersion. (English) Zbl 1468.35179

Summary: We study peakon, cuspon, compacton, and loop solutions for the three-dimensional Kadomtsev-Petviashvili equation (3DKP\((3,2)\) equation) with nonlinear dispersion. Based on the method of dynamical systems, the 3DKP\((3,2)\) equation is shown to have the parametric representations of the solitary wave solutions such as peakon, cuspon, compacton, and loop solutions. As a result, the conditions under which peakon, cuspon, compacton, and loop solutions appear are also given.


35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
Full Text: DOI


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