Solutions of the Modified Chiral Model in (2+1) Dimensions

TL;DR

This paper presents a method to find classical solutions of the modified chiral model in 2+1 dimensions by decomposing the problem into simpler first-order equations involving time-dependent unitons.

Contribution

It introduces a novel approach to solving the modified chiral model using factorization into time-dependent unitons, simplifying the PDE system.

Findings

Solutions correspond to products of time-dependent unitons

Reduction of second-order PDEs to first-order PDEs for unitons

Provides a systematic way to construct solutions

Abstract

This paper deals with classical solutions of the modified chiral model on $R^{2+1}$. Such solutions are shown to correspond to products of various factor which we call time-dependent unitons. Then the problem of solving the system of second-order partial differential equations for the chiral field is reduced to solving a sequence of systems of first-order partial differential equations for the unitons.