Inverse scattering for the massive Thirring model

TL;DR

This paper develops an inverse scattering method using Riemann-Hilbert techniques to solve the massive Thirring model, transforming spectral problems for comprehensive solution reconstruction.

Contribution

It introduces a novel Riemann-Hilbert approach for the inverse scattering transform tailored to the massive Thirring model, handling spectral parameters at zero and infinity.

Findings

Successfully reconstructs solutions from spectral data

Transforms spectral problems for better analytical handling

Provides a framework for solving the massive Thirring model

Abstract

We consider the massive Thirring model in the laboratory coordinates and explain how the inverse scattering transform can be developed with the Riemann-Hilbert approach. The key ingredient of our method is to transform the corresponding spectral problem to the equivalent forms: one is suitable for the spectral parameter at the origin and the other one is suitable for the spectral parameter at infinity. Global solutions to the massive Thirring model are recovered from the reconstruction formulae at the origin and at infinity.