The massive Thirring model: Inverse scattering and soliton resolution

In this paper, the long-time dynamics of the massive Thirring model are investigated. First, the nonlinear steepest descent method for the Riemann-Hilbert problem is explored to obtain the soliton resolution of the solutions to the massive Thirring model with initial data in certain weighted-Sobolev spaces. Second, the asymptotic stability of multi-solitons to the massive Thirring model is established as a conclusion. The main difficulty in studying the massive Thirring model through the inverse scattering method is that the corresponding Lax pair exhibits singularities at the origin and infinity. We overcome the difficulty by introducing a pair of gauge transforms that effectively separate the singularities and exploring the delicate analysis of the inverse scattering method.