N-soliton and rogue wave solutions of (2+1)-dimensional integrable system with Lax pair

Abstract

A new generalized (2[Formula: see text]+[Formula: see text]1)-dimensional model, obtained from the Kadomtsev–Petviashvili (KP) equation considered as a system of nonlinear evolution partial differential equations (PDEs), is introduced. With the usage of the Hirota bilinear method and the KP-hierarchy reduction method, N-soliton solutions of the integrable system are constructed. Considering the case of s[Formula: see text]=[Formula: see text]−1 in the linear differential operators, L1 and L2, and a specific set of parameters, two dark solitons, mixed solutions consisting of soliton-type and periodic waves solution are obtained. Based on the particular definition of the matrix elements, one and two rogue waves solutions expressed in terms of rational functions are derived. It is shown that the fundamental rogue waves are line rogue waves, which is different from the property of the moving line solitons of the soliton equations.