Multi-soliton and Pfaffian solutions of a (2 + 1)-dimensional nonlinear evolution equation via the Jaulent–Miodek hierarchy

Under investigation in this paper is a (2 + 1)-dimensional nonlinear evolution equation generated by the Jaulent–Miodek hierarchy. Via the Hirota bilinear method, multi-soliton solutions of such equation are obtained. Soliton propagation and interactions are analyzed, and both the elastic and inelastic interactions are seen with some parameters selected. Furthermore, it is proved that the equation possesses the N-soliton solutions expressed in terms of Gramm-type Pfaffian, and can be written in the form of a Pfaffian identity.