International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 23, Pages 3711-3725

On symmetries and invariant solutions of a coupled KdV system with variable coefficients

K. Singh and R. K. Gupta

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.


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.