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

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.