Interaction solutions for mKP equation with nonlocal symmetry reductions and CTE method

TL;DR

This paper explores nonlocal symmetry reductions and the CTE method for the mKP equation, deriving interaction solutions including solitons and cnoidal waves, and advancing solution techniques for nonlinear wave interactions.

Contribution

It introduces a method to localize nonlocal symmetries of the mKP equation and applies the CTE method to find explicit interaction solutions.

Findings

Derived nonlocal symmetries via truncated Painleve method

Obtained multi-soliton and interaction solutions

Applied CTE method for explicit wave interactions

Abstract

The nonlocal symmetries for the modified Kadomtsev-Petviashvili (mKP) equation are obtained with the truncated Painleve method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing auxiliary dependent variables. The finite symmetry transformations and similarity reductions related with the nonlocal symmetries are computed. The multi-solitary wave solution and interaction solutions among a soliton and the cnoidal waves of the mKP equation are presented. In the meanwhile, the consistent tanh expansion (CTE) method is applied to the mKP equation. The explicit interaction solutions among a soliton and other types of nonlinear waves such as the cnoidal periodic waves and multiple resonant soliton solutions are given.