Long-time asymptotics for the Massive Thirring model

2018/07/02 by Aaron Saalmann, Saalmann, Aaron
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1807.00623

openalex publication_date 2018/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Long range scattering for the cubic Dirac equation on R¹⁺¹
• Global existence for the derivative NLS equation in the presence of solitons
• Global well-posedness for the derivative nonlinear Schr "odinger\n equation

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