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.

References in corpus (3)

• On a direct approach to quasideterminant solutions of a noncommutative modified KP equation
• Interpolating Dispersionless Integrable System
• Primal-dual algorithm for quasi-static contact problem with Coulomb's friction

Cited by in corpus (5)

• Exact solutions of the Gerdjikov-Ivanov equation using Darboux transformations
• Quasideterminant solutions of the generalized Heisenberg magnet model
• Quasideterminant solutions of an integrable chiral model in two dimensions
• Noncommutative Solitons and Quasideterminants
• Bäcklund Transformations and the Atiyah-Ward ansatz for Noncommutative Anti-Self-Dual Yang-Mills Equations