Conserved quantities and solutions of a (2+1)(2+1)-dimensional H a ˇ r a ˇ gus-Courcelle–Il’ichev model

In this paper we study a (2+1)(2+1)-dimensional Haˇraˇgus-Courcelle–Il’ichev equation (HCI) that models gravity–capillary and flexural-gravity waves. This equation is a generalization of the Kadomtsev–Petviashvili equation, and is obtained due to the presence of certain surface effects. We obtain analytic solutions of the HCI equation by using the Lie symmetry method along with the auxiliary equation method. The solutions obtained are the solitary, cnoidal and snoidal wave solutions. In addition to this we derive the conservation laws of the underlying equation by using the multiplier approach.