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

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.