Darboux transformation of the generalized coupled dispersionless integrable system

Abstract

The Darboux transformation on matrix solutions to the generalized coupled dispersionless integrable system based on some non-abelian Lie group, is studied and the solutions are shown to be expressed in terms of quasideterminants. As an explicit example, the Darboux transformation on scalar solutions to the system based on the Lie group SU(2) is discussed in detail and the solutions are shown to be expressed as ratios of determinants.