Nonlinear Schrodinger equations under random nonlinearity managementPhysics Letters A (2009)
AbstractWe 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.
Publication DateMarch 30, 2009
Citation InformationQY Chen, PG Kevrekidis and BA Malomed. "Nonlinear Schrodinger equations under random nonlinearity management" Physics Letters A Vol. 373 Iss. 15 (2009)
Available at: http://works.bepress.com/panos_kevrekidis/124/