Perturbation theory for the nonlinear Schrodinger equation with a random potential

作者：Fishman Shmuel^*; Krivolapov Yevgeny; Soffer Avy

来源：Nonlinearity, 2009, 22(12): 2861-2887.

DOI：10.1088/0951-7715/22/12/004

A perturbation theory for the nonlinear Schrodinger 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.

• 出版日期2009-12