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

We investigate symmetries and reductions of a coupled KdV system with variable coefficients. The infinitesimals of the groupof transformations which leaves the KdV system invariant andthe admissible forms of the coefficients are obtained using thegeneralized symmetry method based on the Fréchet derivative ofthe differential operators. An optimal system of conjugacyinequivalent subgroups is then identified with the adjoint actionof the symmetry group. For each basic vector field in the optimalsystem, the KdV system is reduced to a system ofordinary differential equations, which is further studied with theaim of deriving certain exact solutions