ABSTRACT
We study the long-time behavior of small (in ) solutions of discrete nonlinear Schrödinger equations with potential. In particular, we are interested in the case that the corresponding discrete Schrödinger operator has exactly two eigenvalues. We show that under the nondegeneracy condition of Fermi Golden Rule, all small solutions decompose into a nonlinear bound state and dispersive wave. We further show the instability of excited states and generalized equipartition property.
2010 Mathematics Subject Classification:
Acknowledgments
The author thank valuable suggestions from Scipio Cuccagna and Kenji Nakanishi. Further, he is grateful for helpful comments given by the anonymous referees to improve the presentation of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.