Symmetry, Integrability and Exact Solutions of a Variable-Coefficient Korteweg-de Vries (vcKdV) Equation
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چکیده
In this paper, a variable-coefficient Korteweg-de Vries (vcKdV) equation which was proposed to describe the propagation of weakly nonlinear waves in water of variable depth is investigated in detail. Firstly, the Lie point symmetries and some group invariant solutions of this equation are presented. Furthermore, the integrability property of this variable-coefficient equation is studied following the Painlevé test of partial differential equations and an integrability condition is obtained. Following this condition, some meaningful exact solutions are obtained via the truncated auto-Bäcklund transformation and the mapping transformation method.
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تاریخ انتشار 2012