Long time dynamics of highly concentrated solitary waves for the nonlinear Schroedinger equation
Analysis of PDEs
2013-12-20 v1 Mathematical Physics
math.MP
Abstract
In this paper we study the behavior of solutions of a nonlinear Schroedinger equation in presence of an external potential, which is allowed to be singular at one point. We show that the solution behaves like a solitary wave for long time even if we start from a unstable solitary wave, and its dynamics coincide with that of a classical particle evolving according to a natural effective Hamiltonian.
Keywords
Cite
@article{arxiv.1312.5463,
title = {Long time dynamics of highly concentrated solitary waves for the nonlinear Schroedinger equation},
author = {Claudio Bonanno},
journal= {arXiv preprint arXiv:1312.5463},
year = {2013}
}
Comments
13 pages