Constructing the soliton solutions for the<i>N</i>= 1 supersymmetric KdV hierarchy

Abstract

We construct the soliton solutions for N = 1 supersymmetric KdV equations. Our starting point is the bilinear transcription of the latter using the super-bilinear operators. We show explicitly the form of the two- and three-soliton solution and give the procedure for constructing the higher ones. The main difference of those solitons with the classical case is that their fermionic part becomes dressed through the interaction. Our approach allows us to compute this dressing in an explicit way.