TY - JOUR

T1 - Nonlinear Schrödinger equations under random nonlinearity management

AU - Chen, Qian Yong

AU - Kevrekidis, P. G.

AU - Malomed, Boris A.

PY - 2009/3/30

Y1 - 2009/3/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=61349204470&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2009.02.034

DO - 10.1016/j.physleta.2009.02.034

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AN - SCOPUS:61349204470

SN - 0375-9601

VL - 373

SP - 1361

EP - 1367

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 15

ER -