Soliton solutions for the super mKdV and sinh-Gordon hierarchy

The dressing and vertex operator formalism is emploied to study the soliton solutions of the N = I super mKdV and sinh-Gordon models. Explicit two and four vertex solutions are constructed. The relation between the soliton solutions of both models is verified. (c) 2006 Elsevier B.V. All rights reserved.

A class of soliton solutions for the N=2 super mKdV/Sinh-Gordon hierarchy

Employing 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 them KdV/sinh-Gordon hierarchy properties we generate the solutions of the N = 2 super sinh-Gordon as well.