Soliton Resonances of the Nonisospectral Modified Kadomtsev-Petviashvili Equation

In the process of searching for explicit solutions, quite a few systematic methods have been developed, such as inverse scattering transformation [1], Darboux transformations [2], Hirota’s bilinear method [3-5], and so on. Among them, the bilinear method first proposed by Hirota provides us with a comprehensive approach to construct exact solutions of nonlinear evolution equations (NEEs). Meanwhile, as the interacting of the solution, soliton resonance has been studied in many papers. Miles obtained resonantly interacting solitary waves of KP equation [6], these solutions are coherent structures that describe the diffraction of a soliton at a corner, and suggest that, under certain conditions, a KP soliton can’t turn at a convex corner without separating or otherwise losing its identity. Thus, these structures provide a solution of the problem of “Mach reflection” in water waves, and this phenomenon is now known as soliton resonance. Asymptotic analysis is a very important tool in studying the behaviors of soliton solutions, we call the asymptotic line soliton solutions as and as the incoming and outgoing line soliton solutions, respectively. The amplitudes, directions and even the number of incoming solitons are in general different from those of the outgoing ones, when resonance occurs two soliton solutions under certain condition resonate and create a new soliton solution. y   y  