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Symmetry reduced and new exact non-traveling wave solutions of potential Kadomtsev-Petviashvili equation with \(p\)-power. (English) Zbl 1203.35250

Summary: With the aid of Maple symbolic computation and Lie group method, PKP\(p\) equation is reduced to some \((1+1)\)-dimensional partial differential equations, in which there are linear PDE with constant coefficients, nonlinear PDE with constant coefficients, and nonlinear PDE with variable coefficients. Using the separation of variables, homoclinic test technique and auxiliary equation methods, we obtain new abundant exact non-traveling solution with arbitrary functions for the PKP\(p\).

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
35C07 Traveling wave solutions

Software:

Maple
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Full Text: DOI

References:

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