Darboux polynomial matrices: the classical Massive Thirring Model as study case

TL;DR

This paper introduces a new polynomial algorithm for constructing Darboux matrices, demonstrated on the classical Massive Thirring Model, enhancing solution methods for integrable PDEs with symmetry considerations.

Contribution

A novel polynomial algorithm for Darboux matrix construction is developed and applied to the Massive Thirring Model, integrating symmetry group analysis.

Findings

Successfully applied the algorithm to the Massive Thirring Model

Enhanced the explicit solution construction for integrable PDEs

Demonstrated the role of symmetry groups in solution methods

Abstract

One way of constructing explicit expressions of solutions of integrable systems of Partial Differential Equations (PDEs) goes via the Darboux method. This requires the construction of Darboux matrices. Here we introduce a novel algorithm to obtain such matrices in polynomial form. Our method is illustrated by applying it to the classical Massive Thirring Model (MTM), and by combining it with the Dihedral group of symmetries possessed by this model.