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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 {\tt 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$p$.

35Q53KdV-like (Korteweg-de Vries) equations
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
37K30Relations of infinite-dimensional systems with algebraic structures
35C07Traveling wave solutions of PDE
Full Text: DOI
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