Long-time asymptotics for the Massive Thirring model

TL;DR

This paper analyzes the long-time behavior of solutions to the massive Thirring model, showing convergence to linear solutions or multi-solitons depending on initial data, using advanced inverse scattering methods.

Contribution

It establishes the long-time asymptotics for the massive Thirring model, including soliton resolution, employing nonlinear steepest descent and recent inverse scattering techniques.

Findings

Solutions with soliton-free data converge to linear solutions with phase correction.

Initial data supporting finitely many solitons evolve into multi-soliton solutions.

The paper confirms soliton resolution for the massive Thirring model.

Abstract

We consider the massive Thirring model and establish pointwise long-time behavior of its solutions in weighted Sobolev spaces. For soliton-free initial data we can show that the solution converges to a linear solution modulo a phase correction caused by the cubic nonlinearity. For initial data that support finitely many solitons we obtain long-time behavior in the form of a multi-soliton which in turn splits into a sum of localized solitons. This phenomenon is known as soliton resolution. The methods we will is the nonlinear steepest descent of Deift and Zhou and the paper also relies on recent progress in the inverse scattering transform for the massive Thirring model.