# American Institute of Mathematical Sciences

January  2017, 37(1): 295-336. doi: 10.3934/dcds.2017013

## Mixed dimensional infinite soliton trains for nonlinear Schrödinger equations

 1 Institute of Mathematics, Academia Sinica, Taipei, Taiwan 2 Department of Mathematics, University of British Columbia, Vancouver BC Canada V6T 1Z2, Canada 3 Center for Advanced Study in Theoretical Sciences, National Taiwan University, Taipei, Taiwan

Received  August 2015 Revised  August 2016 Published  November 2016

Fund Project: Lin is currently a postdoctor at Department of Mathematics, National Cheng Kung University, Tainan, Taiwan. Tsai’s research is supported in part by NSERC grant 261356-13.

In this note we construct mixed dimensional infinite soliton trains, which are solutions of nonlinear Schrödinger equations whose asymptotic profiles at time infinity consist of infinitely many solitons of multiple dimensions. For example infinite line-point soliton trains in 2D space, and infinite plane-line-point soliton trains in 3D space. This note extends the works of Le Coz, Li and Tsai [6,7], where single dimensional trains are considered. In our approach, spatial L bounds for lower dimensional trains play an essential role.

Citation: Liren Lin, Tai-Peng Tsai. Mixed dimensional infinite soliton trains for nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems - A, 2017, 37 (1) : 295-336. doi: 10.3934/dcds.2017013
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