On the line-soliton solutions of a coupled modified Kadomtsev–Petviashvili system in two-layer shallow water

Abstract

In this paper, the line-soliton solutions of a coupled modified Kadomtsev–Petviashvili (MKP) equation are studied. Based on the tau-functions and Grassmannian Gr(N,M), we present and study the coupled modified Kadomtsev–Petviashvili equation and its coupled soliton solutions v and vˆ which can describe two layers shallow water. By giving examples and theoretical analysis, we give a general classification of the structures of coupled soliton solutions v and vˆ. At the same time, we describe the solutions v, vˆ by Le-diagram, chord diagram and analyze the influence of parameter ϵ on the solutions v, vˆ.