Some exact solutions and infinite conservation laws of an extended KdV integrable system

In this paper, we investigate some symmetries and Lie-group transformations of an integrable system by using the symmetry analysis method. It follows that the resulting similarity solutions are obtained by applying the characteristic equations of the symmetries. By applying the software Maple,we work out some exact solutions of the generalized KdV system, including the rational solutions, the periodic solutions, the dark soliton solutions, and so on. Finally, we make use of the self-adjoint operators to investigate the nonlinear self-adjointness and the conservation laws of the generalized KdV integrable system.