Perturbation theory for the Nonlinear Schroedinger Equation with a random potential

Details Perturbation theory for the Nonlinear Schroedinger Equation with a random potential Perturbation theory for the Nonlinear Schroedinger Equation with a random potential

2009-01-30

arxiv.org/abs/0901.4951v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

30 pages, 7 figures, accepted to Nonlinearity

Scientific paper

A perturbation theory for the Nonlinear Schroedinger Equation (NLSE) 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.

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