ИСТИНА

To perform an investigation of optical bullets in a quadratically non- linear planar waveguide we use quasi-optical approach. This method yields a system of multi-dimensional nonlinear parabolic equations with coordinate- dependent coefficients. We derive the integrals of motion inherent for the system. Applying the averaged Lagrangian method, we deduce an approxi- mate soliton solution representing a two-component light bullet and predict four scenarios of bullet formation depending on the sign of nonlinearity and waveguide geometry. To investigate numerically the regimes of the formation and propagation of two-component optical bullets we construct a conserva- tive difference scheme based on the Crank-Nicolson method. To compute the solution on the next layer along the propagation coordinate we use a multi- step effective iterative solver. This method allows us to carry out an accurate and efficient modeling of the investigated processes. Basing on the computa- tion results, we discuss the analytically predicted scenarios of the formation and propagation of light bullets.