Solutions and lax pairs based on bilinear bäcklund transformations of some supersymmetric equations

Abstract

The paper investigates solutions and Lax pairs through bilinear Bäcklund transformations for some supersymmetric equations. We derive variety of solutions from the known bilinear Bäcklund transformations. Besides, using the gauge invariance of (super) Hirota bilinear derivatives we may get deformed bilinear Bäcklund transformations and consequently deformed Lax pairs with fermionic parameters. Examples are the N = 1 supersymmetric KdV equation and the N = 2 supersymmetric KdV 1 equation. © L. Huang and D.-J. Zhang.