Finite and Infinite Soliton and Kink-soliton Trains of Nonlinear Schr?dinger Equations

摘要

We will first review known results on multi-solitons of dispersive partial differential equations, which are special solutions behaving like the sum of many weaklyinteracting solitary waves. We will then describe our recent joint work with Dong Li on nonlinear Schr?dinger equations: Assuming the composing solitons have sufficiently large relative speeds, we prove the existence and uniqueness of a soliton train which is a multi-soliton composed of infinitely many solitons. In the 1D case, we can add to the infinite train an additional half-kink, which is a solution with a non-zero background at minus infinity.