Abstract:
The propagation of the solitary waves in the Bragg grating formed by array of thin dielectric films is considered. We assume that the thin films of contain the resonant molecules, which are evolved according to two-level atoms model, which is used to description of the coherent optical pulses propagation. There the alternative derivation of the Mantsyzov's equations is represented.

Abstract:
An interaction of electromagnetic field with metamaterial thin film containing split-ring resonators with Josephson junctions is considered. It is shown that dynamical self-inductance in a split rings results in reduction of magnetic flux through a ring and this reduction is proportional to a time derivative of split ring magnetization. Evolution of thin film magnetization taking into account dynamical self-inductance is studied. New mechanism for excitation of waves in one dimensional array of split-ring resonators with Josephson junctions is proposed. Nonlinear magnetic susceptibility of such thin films is obtained in the weak amplitude approximation.

Abstract:
We consider the Bose-Einstein condensate trapped in optical lattice, which is formed from two kinds of deep potentials. The tight-binding approximation was used. Steady state distribution of the probability amplitudes and the site population in the one dimensional optical superlattice were found. It was shown that this solution of the equations which describe the dynamics of the Bose-Einstein condensate in superlattice is unstable at the sufficiently high density of the bosons. The expression for increment of the modulational instability was found on base of the linear stability analysis. Numerical simulation demonstrates the evolution of the steady state distributions of bosons into the space array of the solitary peaks before the chaotic regime generation.

Abstract:
The nonlinear polariton transmission, reflection and trapping by a defect in the resonantly absorbing Bragg grating (RABG) is demonstrated in numerical simulation. It is shown that the wide defect under some conditions could effectively serve as microresonator for polaritonic wave storage. The three types of the defect such as microcavity, groove and stripe are considered. Capture the electromagnetic field inside the microcavity (with no resonant nanoparticles) placed in the RABG is observed, as well as stuck of trapped polarization modes to the defect edges for the groove (defect span with reduced density of nanoparticles) and for the stripe with relatively increased density. Strong radiation reflection and adhered propagation of the polarization mode along the first edge of the stripe with high density of resonant atoms is exhibited by numerical computation.

Abstract:
We consider some nonlinear phenomena in metamaterials with negative refractive index properties. Our consideration includes a survey of previously known results as well as identification of the phenomena that are important for applications of this new field. We focus on optical behavior of thin films as well as multi-wave interactions.

Abstract:
Propagation of extremely short pulses of electromagnetic field (electromagnetic spikes) is considered in the framework of the total Maxwell-Duffing model where anharmonic oscillators with cubic nonlinearities (Duffing model) represent the material medium and wave propagation is governed by the 1-d bidirectional Maxwell equations. This system of equations has a one parameter family of exact analytical solutions representing an electromagnetic spike propagating on a zero or a nonzero background. We find that the total Maxwell-Duffing equations can be written as a system in bilinear form and that the one-soliton solution of this system coincides with the steady state solution obtained previously.

Abstract:
The excitation of a thin layer of two-level permanent dipole moment atoms by ultimately short (less than field oscillation period) electromagnetic pulses (videopulse) is observed. The numerical analysis of matter equations free of rotating wave approximation and relaxation reveals a strong affect of local field and Stark effect on temporal behavior of transmitted field. Specifically it is demonstrated that a dense film irradiated by videopulse emits a short response with a delay much longer even than the characteristic cooperative time of atom ensemble. It is supposed that the local field in the thin layer of permanent dipole atoms is able to re-pump the atomic subsystem. The close analogy to nonlinear pendulum motion is discuused.

Abstract:
In this paper we theoretically study propagation of steady state ultrashort pulse in dissipative medium. We considered two cases (i) medium consists of lossy metallic nanostructures embedded into a gain material and (ii) the gain material is embedded directly into the nanostructures. We found the shape and velocity of an optical pulse coupled with the polarization wave.

Abstract:
We discuss a novel kind of nonlinear coupler with one channel filled with a negative index material (NIM). The opposite directionality of the phase velocity and the energy flow in the NIM channel facilitates an effective feedback mechanism that leads to optical bistability and gap soliton formation.

Abstract:
We consider the electromagnetic waves propagating in the system of coupled waveguides. One of the system components is a standard waveguide fabricated from nonlinear medium having positive refraction and another component is a waveguide produced from an artificial material having negative refraction. The metamaterial constituting the second waveguide has linear characteristics and a wave propagating in the waveguide of this type propagates in the direction opposite to direction of energy flux. It is found that the coupled nonlinear solitary waves propagating both in the same direction are exist in this oppositely-directed coupler due to linear coupling between nonlinear positive refractive waveguide and linear negative refractive waveguide. The corresponding analytical solution is found and it is used for numerical simulation to illustrate that the results of the solitary wave collisions are sensible to the relative velocity of the colliding solitary waves.