A Class of Soliton Solutions for the N=2 Super mKdV/Sinh-Gordon Hierarchy

TL;DR

This paper constructs a new class of soliton solutions for the N=2 super mKdV and sinh-Gordon equations using Hirota's method, demonstrating their relation to supersymmetric equations and generalizing previous solutions.

Contribution

It introduces a novel class of solutions for N=2 super integrable equations using Hirota's method and connects them via super Miura transformation.

Findings

Solutions satisfy two copies of N=1 supersymmetric mKdV equations.

Solutions of N=2 super KdV are obtained and generalized.

Solutions of N=2 super sinh-Gordon are generated from hierarchy properties.

Abstract

Employing the Hirota's method, a class of soliton solutions for the N=2 super mKdV equations is proposed in terms of a single Grassmann parameter. Such solutions are shown to satisfy two copies of N=1 supersymmetric mKdV equations connected by nontrivial algebraic identities. Using the super Miura transformation, we obtain solutions of the N=2 super KdV equations. These are shown to generalize solutions derived previously. By using the mKdV/sinh-Gordon hierarchy properties we generate the solutions of the N=2 super sinh-Gordon as well.