Small data scattering for the nonlinear Schr\"odinger equation on product spaces

Nikolay Tzvetkov; Nicola Visciglia

Small data scattering for the nonlinear Schr\"odinger equation on product spaces

Analysis of PDEs 2011-03-21 v2

Authors: Nikolay Tzvetkov , Nicola Visciglia

Abstract

We consider the cubic nonlinear Schr\"odinger equation, posed on $\R^n\times M$ , where $M$ is a compact Riemannian manifold and $n\geq 2$ . We prove that under a suitable smallness in Sobolev spaces condition on the data there exists a unique global solution which scatters to a free solution for large times.

Keywords

nonlinear schrödinger equation schrödinger equation scattering theory

Cite

@article{arxiv.1011.6185,
  title  = {Small data scattering for the nonlinear Schr\"odinger equation on product spaces},
  author = {Nikolay Tzvetkov and Nicola Visciglia},
  journal= {arXiv preprint arXiv:1011.6185},
  year   = {2011}
}

Comments

10 pages, slightly revised version, to appear on Comm. PDE

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