The Nonlinear Schroedinger Equation: Existence, Stability and Dynamics of Solitons

Details The Nonlinear Schroedinger Equation: Existence, Stability and Dynamics of Solitons The Nonlinear Schroedinger Equation: Existence, Stability and Dynamics of Solitons

2010-12-27

arxiv.org/abs/1012.5663v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper we present some recent results concerning the ex- istence, the stability and the dynamics of solitons occurring in the nonlinear Schroedinger equation when the parameter h -> 0. We focus on the role played by the Energy and the Charge in the existence, the stability and the dynamics of solitons. Moreover, we show that, under suitable assumptions, the soliton approximately follows the dynamics of a point particle.

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