%0 Journal Article
%T Freezing of energy of a soliton in an external potential
%A Dario Bambusi
%A Alberto Maspero
%J Physics
%D 2015
%I arXiv
%X In this paper we study the dynamics of a soliton in the generalized NLS with a small external potential $\epsilon V$ of Schwartz class. We prove that there exists an effective mechanical system describing the dynamics of the soliton and that, for any positive integer $r$, the energy of such a mechanical system is almost conserved up to times of order $\epsilon^{-r}$. In the rotational invariant case we deduce that the true orbit of the soliton remains close to the mechanical one up to times of order $\epsilon^{-r}$.
%U http://arxiv.org/abs/1503.08608v1