The thesis proposes a class for the new economic 3-3-1 model, called a simple 3-3-1 model, in order to address the mentioned problems. The simple 3-3-1 model considers the simplest lepton sector and the scalar sector.

Research purpose: to build an analytical model representing the cross Kerr nonlinear coefficient of a four-energy quantum system in the inverse Y configuration in the presence of the Doppler effect. Apply the analytical results to the case of 87Rb at room temperature. Studying the ability to control and enhance the cross Kerr nonlinearity according to the parameters of the associated laser field and the temperature of the environment.

The studied object is the Kerr nonlinear optical systems and optical resonator tworing systems linear coupling with the presence of linear gain and nonlinear loss.

Purpose: Proposing an optical switches model that integrates both optical-magnetic switches and all optical switching in a degenerated two-levels atomic medium; Proposing a model to control the ultraslow group velocity of light soliton and dark soliton in a degenerated two-levels atomic medium.

Research purpose: to build an analytical model describing the dependence of the optical properties (absorption, dispersion, group velocity and group delay) of the three configuration energy level system Λ, Ξ and V according to the following parameters: control parameters (intensity, frequency, polarization and relative phase) of the laser fields.

The main results and new points of this thesis are: The effective emissivity of the diffuse and isothermal cylindrical - inner - cone cavity has been calculated using the polynomial interpolation technique for the angle factor integrals describing the radiation exchange inside the cavity. The interpolation - calculated results are approximately accurate in comparison with those obtained by the analytical methods. This approach is a rather new in the practice of cavity effective emissivity calculation.