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2015•Journal of Applied Analysis & ComputationOpen access

PEAKON, PSEUDO-PEAKON, LOOP, AND PERIODIC CUSP WAVE SOLUTIONS OF A THREE-DIMENSIONAL 3DKP(2, 2) EQUATION WITH NONLINEAR DISPERSION

Hai‐Xia Zhao, Lijing Qiao, Shengqiang Tang

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Abstract

In this paper, we study the three-dimensional Kadomtsev-Petviashvili equation (3DKP(m, n)) with nonlinear dispersion for m=n=2. By using the bifurcation theory of dynamical systems, we study the dynamical behavior and obtain peakon, pseudo-peakon, loop and periodic cusp wave solutions of the three-dimensional 3DKP(2, 2) equation. The parameter expressions of peakon, pseudo-peakon, loop and periodic cusp wave solutions are obtained and numerical graph are provided for those peakon, pseudo-peakon, loop and periodic cusp wave solutions.

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What this paper is about

In this paper, we study the three-dimensional Kadomtsev-Petviashvili equation (3DKP(m, n)) with nonlinear dispersion for m=n=2. By using the bifurcation theory of dynamical systems, we study the dynamical behavior and obtain peakon, pseudo-peakon, loop and periodic cusp wave solutions of the three-dimensional 3DKP(2, 2) equation. The parameter expressions of peakon, pseudo-peakon, loop and periodic cusp wave solutions are obtained and numerical graph are provided for those peakon, pseudo-peakon, loop and periodic cusp wave solutions.

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Available abstract

In this paper, we study the three-dimensional Kadomtsev-Petviashvili equation (3DKP(m, n)) with nonlinear dispersion for m=n=2. By using the bifurcation theory of dynamical systems, we study the dynamical behavior and obtain peakon, pseudo-peakon, loop and periodic cusp wave solutions of the three-dimensional 3DKP(2, 2) equation. The parameter expressions of peakon, pseudo-peakon, loop and periodic cusp wave solutions are obtained and numerical graph are provided for those peakon, pseudo-peakon, loop and periodic cusp wave solutions.

Key concepts: Peakon, Cusp (singularity), Dispersion (optics), Nonlinear system, Mathematical analysis, Mathematics, Physics, Optics

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PEAKON, PSEUDO-PEAKON, LOOP, AND PERIODIC CUSP WAVE SOLUTIONS OF A THREE-DIMENSIONAL 3DKP(2, 2) EQUATION WITH NONLINEAR DISPERSION — Research Paper | ScholarLens