Perturbation theory for the nonlinear Schrödinger equation with a random potential

Shmuel Fishman, Yevgeny Krivolapov, Avy Soffer

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

A perturbation theory for the nonlinear Schrödinger equation in 1D on a lattice was developed. The small parameter is the strength of the nonlinearity. For this purpose secular terms were removed and a probabilistic bound on small denominators was developed. It was shown that the number of terms grows exponentially with the order. The results of the perturbation theory are compared with numerical calculations. An estimate on the remainder is obtained and it is demonstrated that the series is asymptotic.

Original languageEnglish
Pages (from-to)2861-2887
Number of pages27
JournalNonlinearity
Volume22
Issue number12
DOIs
StatePublished - 30 Nov 2009
Externally publishedYes

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