Narrow Results

We consider the nonlinear excitation localized near the thin layer with nonlinear properties separated by different nonlinear media. The excitations are described by nonlinear Schrödinger equation (NLSE) with nonlinear potential. The problem is reduced to the solution of the NLSE with the boundary conditions of a special kind. We obtain the exact solutions of NLSEs satisfying the boundary conditions. We show that the existence of nonlinear localized excitations of four types is possible in a wide energy range. We derive the energy of localized excitations in the explicit form in the long-wave approximation. The conditions of localized state existence are found.

In this paper, the new type of coupled states localized near the nonlinear boundary media and propagating along it are considered. The boundary of nonlinear media with different parameters of anharmonicity of interatomic interaction creates a disturbance of medium characteristic. It is expected that the particle has a complex linear law of dispersion with several branches of different parameters in a model proposed in this paper. The problem is reduced to the solution of the nonlinear Schrödinger equation with boundary conditions for a special kind. Explicit solutions of nonlinear Schrödinger equations satisfying the boundary conditions were found. It is shown that the existence of nonlinear localized excitations of several types is possible. They have a soliton-like profile in the direction perpendicular to the boundary. The structure and shape of the localized states is determined by the anharmonicity parameters and the intensity of interaction of the excitations with the plane defect. The equations determining the energy of the wave localized along the media boundary for a fixed direction of its wave vector are derived. Dependences of the wave numbers from the parameters of the system for localized states in various private cases are explicitly expressed.

We analyze guided waves in the linear media separated nonlinear interface. The mathematical formulation of the model is a one-dimensional boundary value problem for the nonlinear Schrödinger equation. The Kerr type nonlinearity in the equation is taken into account only inside the waveguide. We show that the existence of nonlinear stationary waves of three types is possible in defined frequency ranges. We derive the frequency of obtained stationary states in explicit form and find the conditions of its existence. We show that it is possible to obtain the total wave transition through a plane defect. We determine the condition for realizing of such a resonance. We obtain the reflection and transition coefficients in the vicinity of the resonance. We establish that complete wave propagation with nonzero defect parameters can occur only when the nonlinear properties of the defect are taken into account.

We analyze the localization in three-layered symmetric structure consisting of linear layer between focusing nonlinear media separated by nonlinear interfaces. The mathematical formulation of the model is a one-dimensional boundary value problem for the nonlinear Schrödinger equation. We find nonlinear localized states of two types of symmetry. We derive the energies of obtained stationary states in explicit form. We obtain the localization energies as exact solutions of dispersion equations choosing the amplitude of the interface oscillations as a free parameter. We analyze the conditions of their existence depending on the combination of signs of interface parameters.

We describe the non-symmetrical spatial-distributed electric field near the thin optic layer with nonlinear properties that separated two focusing and defocusing media with Kerr-type nonlinearity differing by values of refractive index. The nonlinear Schrödinger equation (NLSE) with nonlinear potential containing two parameters describes the distribution of electric field strength in adiabatic approximation. The problem is reduced to the solution of NLSEs at the half-spaces with the nonlinear boundary conditions at the interface plane. We obtain five new types of nonlinear stationary states describing the confinement effect of electric field strength across the interface. The field confinement effect is the localization of nonlinear spatially periodic wave during the transition from a one half-space to another one where the field distribution is monotonically damping from the interface. We derive and analyze the frequencies of field confinement effect possibility in dependence of media and interface characteristics.

The nonlinear surface waves propagating along the ultra-thin-film layers with nonlinear properties separating three nonlinear media layers are considered. The model based on a stationary nonlinear Schrödinger equation with a nonlinear potential modeling the interaction of a wave with the interface in a short-range approximation is proposed. We concentrated on effects induced by the difference of characteristics of the layers and their two interfaces. The surface waves of three types exist in the system considered. The dispersion relations determining the dependence of surface waves energy on interface intensities and medium layer characteristics are obtained and analyzed. The localization energy is calculated in explicit form for many difference cases. The conditions of the wave localization on dependence of the layer and interface characteristics are derived. The surface waves with definite energies in specific cases existing only in the presence of the interface nonlinear response are found. All results are obtained in an explicit analytical form.