Two types of generalized integrable decompositions and new solitary-wave solutions for the modified Kadomtsev-Petviashvili equation with symbolic computation

TL;DR

This paper decomposes the modified Kadomtsev-Petviashvili (mKP) equation into two integrable hierarchies, constructs Darboux transformations for each, and derives new solitary-wave solutions with stability analysis using symbolic computation.

Contribution

It introduces two types of integrable decompositions of the mKP equation and constructs explicit Darboux transformations for generating new solutions.

Findings

Four new solitary-wave solution families are obtained.

Explicit solutions are generated recursively via Darboux transformations.

Stability of the solutions is analyzed.

Abstract

The modified Kadomtsev-Petviashvili (mKP) equation is shown in this paper to be decomposable into the first two soliton equations of the 2N-coupled Chen-Lee-Liu and Kaup-Newell hierarchies by respectively nonlinearizing two sets of symmetry Lax pairs. In these two cases, the decomposed (1+1)-dimensional nonlinear systems both have a couple of different Lax representations, which means that there are two linear systems associated with the mKP equation under the same constraint between the potential and eigenfunctions. For each Lax representation of the decomposed (1+1)-dimensional nonlinear systems, the corresponding Darboux transformation is further constructed such that a series of explicit solutions of the mKP equation can be recursively generated with the assistance of symbolic computation. In illustration, four new families of solitary-wave solutions are presented and the relevant stability is analyzed.