Nonlinear Schrödinger equations under random nonlinearity management

Qian Yong Chen, P. G. Kevrekidis, Boris A. Malomed*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider effects of random time modulation of the nonlinearity coefficient on the dynamics of one- and two-dimensional (1D and 2D) solitary waves in the nonlinear Schrödinger equation (NLSE). In particular, the cases of a single Gaussian random variable, and a temporally correlated Gaussian process are considered. In the 1D case, we demonstrate the robustness of solitons against the random nonlinearity management. In the 2D case, the share (percentage) of realizations that lead to collapse of a localized pulse is computed, in order to quantify the effect of the randomness in preventing the collapse. Dependences of this share on the mean value, standard deviation, and correlation length of the random process are obtained, and, whenever possible, compared to analytical predictions.

Original languageEnglish
Pages (from-to)1361-1367
Number of pages7
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number15
StatePublished - 30 Mar 2009


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