Fock asymptotics in the problem of diffraction by a moving smooth contour

In the paper the asymptotics are obtained of the solution of the diffraction problem in the Fock region for the incidence of a nonstationary modulated wave on a smooth moving contour. The formulas obtained generalize the solution of V. A. Fock to the stationary problem in a neighborhood of a point of tangency of an ray to the case of a nonstationary wave and a moving scatterer. A new characteristic of the problem is introduced the effective radius of curvature of the contour, depending on the geometric and kinematic properties of the scatterer. The boundaries are established of the applicability of the asymptotic formulas.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institute im. V. A. Steklova AN SSSR, Vol. 195, pp. 69–81, 1991.In conclusion I want to thank the participants of the seminars of LGU and LOMI on the diffraction and propagation of waves for useful discussions.