Abstract

For nonlinear Schrodinger equations, we introduce our results on the construction of special solutions whose time asymptotic profiles consist of infinitely many solitons of more than one dimensions (the so called "mixed dimensional infinite soliton trains"), e.g. line-point soliton trains in 2D space and plane-line-point soliton trains in 3D space. This work is an extension of Le Coz, Li, and Tsai's works on single dimensional cases. We'll try to make clear the general idea of the approach, and explain particular difficulties for mixed dimensional cases.