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Multiple solution profiles to the higher-dimensional Kadomtsev-Petviashvilli equations via Wronskian determinant. (English) Zbl 1151.35421
Summary: Many types of new exact solutions of \((3 + 1)\)-dimensional KP equation are obtained via a unified Wronskian determinant and three linear partial differential equations, which involve many types of multiple solitary wave solutions, rational solutions, and rational-solitary wave solutions. It is shown that the collisions of the obtained multiple solitary wave solutions are elastic, which implies that \((3 + 1)\)-dimensional KP equation admits multisoliton solutions. Moreover the Wronskian formal solutions of \((n + 1)\)-dimensional KP equations are given.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
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