International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 23, Pages 3711-3725
doi:10.1155/IJMMS.2005.3711
On symmetries and invariant solutions of a coupled KdV system with variable coefficients
Department of Mathematics, Jaypee University of Information Technology, Waknaghat, P.O. Dumehar Bani, Kandaghat, Distt. Solan, Pin-173215 (H.P.), India
; Revised 18 October 2005
Copyright © 2005 K. Singh and R. K. Gupta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We investigate symmetries and reductions of a coupled KdV system with variable coefficients. The infinitesimals of the group
of transformations which leaves the KdV system invariant and
the admissible forms of the coefficients are obtained using the
generalized symmetry method based on the Fréchet derivative of
the differential operators. An optimal system of conjugacy
inequivalent subgroups is then identified with the adjoint action
of the symmetry group. For each basic vector field in the optimal
system, the KdV system is reduced to a system of
ordinary differential equations, which is further studied with the
aim of deriving certain exact solutions.