Multi-soliton dynamics in the nonlinear Schrödinger equation

2020/10/21 by Cao, Daomin, Guo, Qing, Zou, Changjun
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.10730

Abstract

In this paper, we study the Cauchy problem of the nonlinear Schrödinger equation with a nontrival potential V_ε(x). In particular, we consider the case where the initial data is close to a superposition of k solitons with prescribed phase and location, and investigate the evolution of the Schrödinger system. We prove that over a large time interval with the maximum time tending to infinity, all k solitons will maintain the shape, and the solitons dynamics can be regarded as an approximation of k particles moving in ℝ^N with their accelerations dominated by ∇ V_ε, provided the barycenters of these solitons do not coincide.

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