Freezing of energy of a soliton in an external potential

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 ${\epsilon }^{-r}$.

References in corpus (1)

• Solitary Wave Dynamics in an External Potential

Cited by in corpus (5)

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• Exponential stability in the perturbed central force problem
• Nekhoroshev theorem for perturbations of the central motion