New exact solutions of the -dimensional KdV equation with variable coefficients

Shen, Shoufeng; Zhang, Jun; Ye, Caier; Pan, Zuliang

doi:10.1016/j.physleta.2005.01.056

Cited by 15 publications

(1 citation statement)

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“…Zhang et al [11] performed Painlevé analysis for (1) and constructed bilinear auto-Bäcklund, analytic solutions in the Wronskian form. Soliton-like solutions, Jacobi elliptic function-like solutions, and other exact solutions have been obtained by the method of auxiliary equations [12][13][14][15]. Elwakil et al [16] used the homogeneous balance method to study the exact solutions of (1).…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

2014

Abstract and Applied Analysis

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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 oft. 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.

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