This article is cited in 1 paper

Symmetry analysis and exact explicit solutions for Kadomtsev–Petviashvili–Burgers equation

Long Wei

Institute of Applied Mathematics and Engineering Computations, Hangzhou Dianzi University, Zhejiang 310018, China

Abstract: We apply the group theory to Kadomtsev–Petviashvili–Burgers (KPBII) equation which is a natural model for the propagation of the two-dimensional damped waves. In correspondence with the generators of the symmetry group allowed by the equation, new types of symmetry reductions are performed. Some new exact solutions are obtained, which can be in the form of solitary waves and periodic waves. Specially, our solutions indicate that the equation may have time-dependent nonlinear shears. Such exact explicit solutions and symmetry reductions are important in both applications and the theory of nonlinear science.

Key words: Kadomtsev–Petviashvili–Burgers equation, Lie symmetry analysis, Symmetry reduction, Exp-function method, exact solution.

UDC: 519.63

Received: 09.11.2009
Revised: 22.03.2011

Language: English

 English version: Computational Mathematics and Mathematical Physics, 2011, 51:8, 1369–1376

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