Zhyla O. Integral equation method in modeling of asymmetric electromagnetic phenomena in an inhomogeneous medium

Object – Airy pulse deformation process in an inhomogeneous and nonstationary medium. Aim – investigation of the propagation of Airy electromagnetic pulses in nonstationary inhomogeneous media. Subject – space-time distribution of an Airy electromagnetic pulse in an inhomogeneous and nonstationary medium. Methods – Volterra method of integral equations of the second kind, resolvent method, methods of mathematical physics. Results – The space-time problem of the transformation of an Airy pulse in an inhomogeneous nonstationary medium is solved by the method of integral equations and resolvent; the analytical expressions describing space-time structure of Airy pulse as a result of its interaction with motionless flat border are received taking into account its initial position in free space; the problem of the transformation of the Airy pulse by the nonstationary boundary of the media, which moves uniformly, is solved; solutions of the problem of the transformation of the Airy pulse after its penetration into the dielectric layer with a constant boundaries and into the dielectric layer, whose boundaries uniformly move with respect to each other, are obtained. Application - development of new practical methods for the development of tasks of optical nonlinear control, manipulation with micro-objections in biochemistry and medicine