Shmuel Fishman et al 2009 Nonlinearity 22 2861 doi:10.1088/0951-7715/22/12/004
Shmuel Fishman1, Yevgeny Krivolapov1 and Avy Soffer2
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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.
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
37K40 Soliton theory, asymptotic behavior of solutions
Issue 12 (December 2009)
Received 26 January 2009, in final form 7 September 2009
Published 30 October 2009
Shmuel Fishman et al 2009 Nonlinearity 22 2861
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