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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.

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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}
}

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13 pages