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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 $\left(1+1\right)$-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-like (Korteweg-de Vries) equations 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies 37K30 Relations of infinite-dimensional systems with algebraic structures 35C07 Traveling wave solutions of PDE
Maple