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arXiv · 1503.08608

Freezing of energy of a soliton in an external potential

Dario Bambusi·Alberto Maspero
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Abstract

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 $\epsilon^{-r}$.

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Dario Bambusi, Alberto Maspero. 2015-03-30. Freezing of energy of a soliton in an external potential. https://doi.org/10.1007/s00220-015-2570-y

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