A discrete generalized coupled dispersionless integrable system and its multisoliton solutions

An integrable discretization of generalized coupled dispersionless (dGCD) integrable system via Lax pair is presented. A Lax pair for the dGCD system is defined. A Darboux transformation is used on the Lax pair to obtain multi-soliton solutions of the dGCD system. The solutions are expressed in terms of quasideterminants. Explicit expressions of discrete one- and two-soliton solutions are obtained for the SU(2) case by using properties of quasideterminants. We also study continuous analogue of the dGCD system by applying continuum limit.