Superfield Bäcklund and Darboux transformations of an \(\mathcal N=1\) supersymmetric coupled dispersionless integrable system

Abstract

We use a superfield Darboux matrix to study Darboux transformations of an \(\mathcal N=1\) supersymmetric coupled dispersionless integrable system. The notion of quasideterminants is used to obtain superfield \(N\)-soliton solutions of that system. A superfield Lax representation is used to obtain a superfield Bäcklund transformation via a set of superfield Riccati equations. The Bäcklund and Darboux transformations are further used to compute explicit expressions for superfield soliton solutions of the supersymmetric coupled dispersionless integrable system.