Abstract
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.
Highlights
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
Nonlinear phenomena play a crucial role in applied mathematics and physics
Summary
Nonlinear phenomena play a crucial role in applied mathematics and physics. Studies of various physical structures of nonlinear dispersive equations had attracted much attention in connection with the important problems that arise in scientific applications. 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. It is well known that the existence of the singular straight lines implies the occurrence of some nonsmooth dynamical behaviors and curve breaking phenomena of the traveling wave solutions of such system, more precisely the so-called peakon and cuspon, and so forth.
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