Backlund transformation and N-soliton solutions for a (2+1)-dimensional nonlinear evolution equation in nonlinear water waves

Under investigation in this paper is a (2+1)-dimensional nonlinear evolution equation generated via the Jaulent-Miodek hierarchy for nonlinear water waves. With the aid of binary Bell polynomials and symbolic computation, bilinear forms and Backlund transformations are derived. N-soliton solutions are obtained through the Hirota method. Soliton propagation is discussed analytically. The bell-shaped soliton, anti-bell-shaped soliton and shock wave can be seen with some parameters selected. Soliton interactions are analyzed graphically: four kinds of elastic interactions are presented: two parallel bell-shaped solitons, two parallel anti-bell-shaped solitons, three parallel bell-shaped solitons and three parallel anti-bell-shaped solitons. We see that (1) the solitons maintain their original amplitudes, widths and directions except for some phase shifts after each interaction, and (2) the smaller the soliton amplitude is, the faster the soliton travels.