New symmetries, group-invariant solutions, linear differential constraints of a generalized Burgers-KdV equation and its reduction

Abstract

All we know that the Burgers-KdV equation is extensively used to study the liquid flow with bubbles and the liquid moving flow in the elastic pipes. In this paper, we obtain the Lie point symmetries, self-nonlinear adjointness of a generalized Burgers-KdV equation (GB-KdVE) are obtained, it follows that the conservation laws are worked out. As a reduction of the GB-KdVE, a Burgers equation with general coefficients is presented, whose new strong symmetry and new nonlocal symmetries are generated, respectively. Furthermore, the noninvariant solutions of the GB-KdVE are produced as well. Finally, we propose the double linear differential constraints for GB-KdVE-type so that some soliton solutions are singled out.