Titlebook: Nonlinearity with Disorder; Proceedings of the T Fatkulla Abdullaev,Alan R. Bishop,Stephanos Pnevma Conference proceedings 19921st edition

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The Nonlinear Schr?dinger Equation on a Disordered Chainamics, and its interplay with nonlinearity. We first review some features of the lattice nonlinear Schr?dinger equation in the absence of disorder and introduce a l-and 2-soliton collective variable approximation. Then we describe the effect of different types of disorder: attractive and repulsive i

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Modulated Dark Soliton: Features of Creation and Propagationsidered in the framework of the perturbation theory based on the inverse scattering technique. Modulations result in both the variation of soliton parameters and creation of new solitons. Corresponding problems are treated analytically. The criterion for the perturbation theory to be valid is stated

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Dynamics of a Stochastically Perturbed ,, Modelroach. The threshold noise strength is found to depend on the initial kink speed. The main effects induced by strong perturbations are subsequently described. Possible explanations of our results are briefly discussed.

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On the Threshold of KdV Soliton Productionarea” pulses, . is established. The following zero area pulses were considered: (1) the rectangular pulse (expression (1)); (2) the “sinusoidal” pulse, U (x, 0) = U. · sinkx, x ∈ (? π /k, π /k); (3) the Rayleigh pulse, U (x, 0) = U. · x · exp (?k. x.).

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One-Dimensional Localization and Wave Propagation in Linear and Nonlinear Mediaon gives rise to the existence of quasi-stationary states in open disordered systems. As a result 1)the random stratified layer has effective waveguide properties, and 2) in nonlinear optical fibers the random input pulse generates soliton-like excitations.