Long-time dynamics of the modified KdV equation

Soliton resolution, roughly speaking, says that any reasonable solution to a disperive equation eventually resolves into a superposition of a radiation component plus a finite number of "nonlinear bound states" or "solitons". Combing ideas from integrable systems and PDEs, I will discuss the soliton resolution and long-time dynamics for the modified Korteweg-de vries (mKdV) equation with initial conditions in some weighted Sobolev spaces.