Solitons, breathers and rational solutions for a (2+1)-dimensional dispersive long wave system

Abstract

In this paper, we investigate a (2+1)-dimensional dispersive long wave system with an arbitrary constant a. Solitons, line breathers, rational solutions and algebraic solitons of the system are constructed based on Hirota’s bilinear method and Kadomtsev–Petviashvili (KP) hierarchy reduction technique. These solutions are expressed in terms of N×N determinant. When the size of the determinant N is odd, solutions on periodic backgrounds are generated. Solutions on constant backgrounds are derived when N is even. By using asymptotic analysis, we elucidate explicit expressions of asymptotic algebraic solitons localized in the straight for the algebraic soliton solutions. As a byproduct, we find lump solutions for an intermediate potential of the system. The effects of constant a are discussed and it is shown that the constant can affect collision of solitons. Dynamics of the obtained solutions are discussed with plots.