Interaction solutions for supersymmetric mKdV-B equation

TL;DR

This paper applies the bosonization and consistent tanh expansion methods to solve the supersymmetric mKdV-B system, deriving interaction solutions among solitons, Painlevé waves, and cnoidal waves, and providing analytical and graphical analysis.

Contribution

It introduces a bosonization approach to simplify supersymmetric equations and develops an auto-B"{a}cklund theorem for interaction solutions, including soliton and wave interactions.

Findings

Derived interaction solutions among solitons, Painlevé waves, and cnoidal waves.

Established an auto-B"{a}cklund theorem for the bosonized system.

Provided analytical and graphical analysis of soliton-cnoidal interactions.

Abstract

The ${\cal N} =1$ supersymmetric mKdV-B system is transformed to a system of coupled bosonic equations by using the bosonization approach. The bosonized supersymmetric mKdV-B (BSmKdV-B) equation can be solved by the usual mKdV equation together with a linear differential equations without fermionic variables. The bosonization approach can thus effectively avoid difficulties caused by anticommutative fermionic fields of the supersymmetric systems. The consistent tanh expansion (CTE) method is applied to the BSmKdV-B equation. An auto-B\"{a}cklund (BT) theorem is obtained by using CTE method. The interaction solutions among solitons and other complicated waves including Painlev\'{e} waves and periodic cnoidal waves are given through an auto-BT theorem. For the soliton-cnoidal interaction solution, two concrete cases are investigated both in analytical and graphical ways by combining the mapping and deformation method.