Solutions of Nonlinear Schrödinger Equation with Two Potential Wells in Linear/Nonlinear Media

In the framework of nonlinear Schrödinger equation, we analytically studied the nonlinear localized states in the system with two potential holes in the cases of linear and nonlinear media in the holes as well as their linear and nonlinear environment. All the possible solutions for the system are found and studied. The frequency dependences of the field amplitudes for all types of possible stationary localized states are obtained

Instabilities and Bifurcations of Nonlinear Impurity Modes

We study the structure and stability of nonlinear impurity modes in the discrete nonlinear Schr{\"o}dinger equation with a single on-site nonlinear impurity emphasizing the effects of interplay between discreteness, nonlinearity and disorder. We show how the interaction of a nonlinear localized mode (a discrete soliton or discrete breather) with a repulsive impurity generates a family of stationary states near the impurity site, as well as examine both theoretical and numerical criteria for the transition between different localized states via a cascade of bifurcations.Comment: 8 pages, 8 figures, Phys. Rev. E in pres

Localized States Near a Nonlinear Optical Waveguide

In the framework of nonlinear Schrödinger equation the soliton states localized near a nonlinear optical waveguide (defect layer) in optically linear medium are investigated. All the possible localized states in such a system are described. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3028