Quasideterminant solutions of an integrable chiral model in two dimensions

TL;DR

This paper employs Darboux transformations to derive multisoliton solutions for a two-dimensional integrable chiral model, expressing solutions via quasideterminants and linking to existing dressing method results.

Contribution

It introduces quasideterminant-based multisoliton solutions for the chiral model, connecting Darboux transformations with the dressing method and Riemann-Hilbert problem.

Findings

Quasideterminant multisoliton solutions are explicitly constructed.

Solutions match those obtained by the dressing method.

The approach provides a new algebraic framework for the model.

Abstract

The Darboux transformation is used to obtain multisoliton solutions of the chiral model in two dimensions. The matrix solutions of the principal chiral model and its Lax pair are expressed in terms of quasideterminants. The iteration of the Darboux transformation gives the quasideterminant multisoliton solutions of the model. It has been shown that the quasideterminant multisoliton solution of the chiral model is the same as obtained by Zakharov and Mikhailov using the dressing method based on the matrix Riemann-Hilbert problem.