Long-time asymptotics 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.

The massive Thirring system in the quarter plane

“…2. By using the nonlinear steepest descent method [39], long-time asymptotics of the solution of the initial value problem of the MT system has been derived recently in [18] with aid of the RH problems established in [17]. We note that the RH problems established in this paper for the IBV problem of the MT system have explicit exponential (x, t)-dependence.…”

“…The MT system (1.1) has been studied by numerous authors from different points of view (for example, see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and references therein). In particular, the inverse scattering transform (IST) for the initial value problem of the MT system was presented in [3][4][5][6][7] and was recently studied in [17].…”