Rational solutions for a [formula omitted]-dimensional nonlinear model in water waves generated by the Jaulent–Miodek hierarchy

Abstract

This paper deals with a (2+1)-dimensional nonlinear evolution equation (NLEE) generated by the Jaulent–Miodek hierarchy for nonlinear water waves via the Hirota’s bilinear method and Pfaffian. First, we construct rational solutions for general bilinear equations, and then convert the target bilinear equations to the general ones to obtain their rational solutions. The Pfaffian plays a role to simplifying the computations compared with the determinant way in the existing literatures. Once the first- and second-order rational solutions have been obtained, the higher-order solutions can be derived by the same token. Figures for the first- and second-order rational solutions are plotted and analyzed. As an application, the rational solutions for the modified Kadomtsev–Petviashvili equation have also been constructed. The method might be used for some other NLEEs to construct their rational solutions.