Massive Thirring Model: Inverse Scattering and Soliton Resolution

TL;DR

This paper analyzes the long-time behavior of the massive Thirring model using inverse scattering, demonstrating soliton resolution and stability of multi-solitons despite singularities in the Lax pair.

Contribution

It applies the nonlinear steepest descent method to the inverse scattering transform for the massive Thirring model, addressing singularities to establish soliton resolution and stability results.

Findings

Soliton resolution for the massive Thirring model established.

Asymptotic stability of multi-solitons demonstrated.

Overcomes singularity issues in the inverse scattering analysis.

Abstract

In this paper the long-time dynamics of the massive Thirring model is investigated. Firstly the nonlinear steepest descent method for Riemann-Hilbert problem is explored to obtain the soliton resolution of the solutions to the massive Thirring model whose initial data belong to some weighted-Sobolev spaces. Secondly, the asymptotic stability of multi-solitons follow as a corollary. The main difficulty in studying the massive Thirring model through inverse scattering is that the corresponding Lax pair has singularities at the origin and infinity. We overcome this difficulty by making use of two transforms that separate the singularities.