# Darboux transformation of the generalized coupled dispersionless integrable system

@article{Hassan2009DarbouxTO, title={Darboux transformation of the generalized coupled dispersionless integrable system}, author={M. I. Hassan}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2009}, volume={42}, pages={065203} }

The Darboux transformation on matrix solutions to the generalized coupled dispersionless integrable system based on a 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.

## 52 Citations

A noncommutative coupled dispersionless system, Darboux transformation and explicit solutions

- Mathematics
- 2014

A noncommutative generalization of coupled dispersionless system has been presented. It has been shown that the system is equivalent to integrable noncommutative sine-Gordon equation. The Darboux…

Darboux transformation and N-soliton solutions for a more general set of coupled integrable dispersionless system

- Physics, Mathematics
- 2011

Quasideterminant solutions of 2-component non–commutative complex coupled integrable dispersionless system

- MathematicsJournal of Physics Communications
- 2018

We present a non–commutative extension of two-component complex coupled integrable disspersionless (NC-CCID) system. We studied matrix Darboux transformation and generate multiple soliton solutions…

Bilinearization and soliton solutions of N=1 supersymmetric coupled dispersionless integrable system

- Physics
- 2017

An N=1 supersymmetric generalization of coupled dispersionless (SUSY-CD) integrable system has been proposed by writing its superfield Lax representation. It has been shown that under a suitable…

Multi-component semi-discrete coupled dispersionless integrable system, its lax pair and Darboux transformation

- Physics, MathematicsCommun. Nonlinear Sci. Numer. Simul.
- 2018

Quasideterminant solutions of 2-component non–commutative complex coupled integrable dispersionless system

- Mathematics
- 2018

Wepresent a non–commutative extension of two-component complex coupled integrable disspersionless (NC-CCID) system.We studiedmatrixDarboux transformation and generate multiple soliton solutions by…

Darboux transformation of a semi-discrete coupled dispersionless integrable system

- Mathematics, PhysicsCommun. Nonlinear Sci. Numer. Simul.
- 2017

On the Dressing Method for the Generalized Coupled Dispersionless Integrable System

- Physics, Mathematics
- 2013

The dressing method of Zakharov and Shabat [Funct. Anal. Appl.8, 226 (1974) and ibid.13, 166 (1980)] has been employed to the generalized coupled dispersionless integrable system in two dimensions.…

Integrability of a Multicomponent Coupled Dispersionless Integrable System

- MathematicsTheoretical and Mathematical Physics
- 2018

We present a multicomponent coupled dispersionless integrable system and show that it is integrable in the sense of the existence of a Lax pair representation and also the existence of an infinite…

DARBOUX TRANSFORMATION AND MULTI-SOLITON SOLUTIONS OF PRINCIPAL CHIRAL AND WZW MODELS

- Mathematics
- 2011

In this paper we present Darboux transformation for the principal chiral and WZW models in two dimensions and construct multi-soliton solutions in terms of quasideterminants. We also establish the…

## References

SHOWING 1-10 OF 36 REFERENCES

An interpolating dispersionless integrable system

- Mathematics, Physics
- 2008

We introduce a dispersionless integrable system which interpolates between the dispersionless Kadomtsev–Petviashvili equation and the hyper-CR equation. The interpolating system arises as a symmetry…

Singularity structure analysis and Hirota's bilinearisation of the coupled integrable dispersionless equations

- Mathematics
- 1997

Darboux Transformations in Integrable Systems

- Mathematics
- 2005

The Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play important…

Integrable hierarchies and dispersionless limit

- Mathematics
- 1995

Analogues of the KP and the Toda lattice hierarchy called dispersionless KP and Toda hierarchy are studied. Dressing operations in the dispersionless hierarchies are introduced as a canonical…

An algebraic method to construct the Darboux matrix

- Mathematics
- 1995

We present an effective procedure to construct the 1‐soliton Darboux matrix. Our approach, based on the Zakharov–Shabat–Mikhailov’s dressing method, is especially useful in the case of non‐canonical…

The dispersionless Lax equations and topological minimal models

- Physics, Mathematics
- 1992

It is shown that perturbed rings of the primary chiral fields of the topological minimal models coincide with some particular solutions of the dispersionless Lax equations. The exact formulae for the…

Solution of the dispersionless Hirota equations

- Physics
- 1995

The dispersionless differential Pay identity is shown to be equivalent to a kernel expansion providing a universal algebraic characterization and solution of the dispersionless Hirota equations. Some…

New Coupled Integrable Dispersionless Equations

- Physics, Mathematics
- 1994

New coupled integrable dispersionless equations are presented and solved by the inverse scattering method.