On the solutions and conservation laws of a coupled KdV system

In this paper Lie symmetry analysis is performed on the coupled KdV system which describes a resonant interaction of two wave modes in a shallow stratified liquid. The similarity reductions and exact solutions with the aid of simplest equation method and Jacobi elliptic function method are obtained based on the optimal systems of one-dimensional subalgebras for the KdV system. In addition, the conservation laws of the coupled KdV system are also derived using the multiplier (and homotopy) approach and a conservation theorem.