Massive Thirring模型的长时间渐近性
Long-time asymptotics for the Massive Thirring model
摘要：
考虑了有质量的Thirring模型，并在加权索伯列夫空间中建立了其解的逐点长时间行为.对于无孤子的初始数据，我们可以证明解收敛到模由立方非线性引起的相位校正的线性解。对于初始数据，支持100多个孤子，我们得到的长时间行为的形式，多孤子，这反过来又分裂成一个本地化孤子的总和。这种现象被称为孤子分辨率。我们将采用Deift和Zhou的非线性最速下降方法，并借鉴了近年来大量Thirring模型的逆散射变换方法。
英文摘要：
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.
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