Abstract and Applied Analysis

Conservation Laws, Symmetry Reductions, and New Exact Solutions of the (2 + 1)-Dimensional Kadomtsev-Petviashvili Equation with Time-Dependent Coefficients

Li-hua Zhang

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Abstract

The (2 + 1)-dimensional Kadomtsev-Petviashvili equation with time-dependent coefficients is investigated. By means of the Lie group method, we first obtain several geometric symmetries for the equation in terms of coefficient functions and arbitrary functions of t. Based on the obtained symmetries, many nontrivial and time-dependent conservation laws for the equation are obtained with the help of Ibragimov’s new conservation theorem. Applying the characteristic equations of the obtained symmetries, the (2 + 1)-dimensional KP equation is reduced to (1 + 1)-dimensional nonlinear partial differential equations, including a special case of (2 + 1)-dimensional Boussinesq equation and different types of the KdV equation. At the same time, many new exact solutions are derived such as soliton and soliton-like solutions and algebraically explicit analytical solutions.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 853578, 13 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412278850

Digital Object Identifier
doi:10.1155/2014/853578

Mathematical Reviews number (MathSciNet)
MR3198264

Citation

Zhang, Li-hua. Conservation Laws, Symmetry Reductions, and New Exact Solutions of the (2 + 1)-Dimensional Kadomtsev-Petviashvili Equation with Time-Dependent Coefficients. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 853578, 13 pages. doi:10.1155/2014/853578. https://projecteuclid.org/euclid.aaa/1412278850


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