Perturbation theory for the Nonlinear Schroedinger Equation with a random potential

Avy Soffer; Shmuel Fishman; Yevgeny Krivolapov

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Perturbation theory for the Nonlinear Schroedinger Equation with a random potential

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arxiv 0901.4951 v2 pith:HOLA2FLJ submitted 2009-01-30 cond-mat.dis-nn

Shmuel Fishman , Yevgeny Krivolapov , Avy Soffer This is my paper

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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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