CLASSICAL NONLINEAR DYNAMICS AND CHAOS OF RAYS IN WAVE-PROPAGATION PROBLEMS IN INHOMOGENEOUS-MEDIA

The geometrical theory of a wave propagation in inhogeneous waveguide media is discussed from the view point of the nonlinear Hamiltonian dynamics. We consider the phenomenon of a spatial nonlinear resonance in the case of periodic inhomogeneities which lead to the appearance of the effective waveguide channel in the vicinity of the resonantray. The following properties of the rays trapped into the nonlinear resonance are considered in detail: the optical path length and the signal transmission speed and their fractal properties. It is shown that the dependences of these parameters on initial coordinates of rays have the form of the "devil's staircase". Using the method of adiabatic invariants we study the propagation of sound rays in the ocean model with a transverse flow. The transverse drift of the rays with respect to the sound propagation direction is described. The conditions for the appearance of the rays chaos in waveguides with periodic longitudinal inhomogeneities are investigated. The conditions of the internal nonlinear resonance and chaos of rays are obtained for a waveguide with two-dimensional cross-section. The relation between the structure of the wavefront and dynamics of rays in waveguides with regular inhomogeneities is investigated. Finally, we discuss the problem of validity of geometric optics in waveguide, in which the spatial nonlinear resonance and chaos of rays are developed, and the relation between this problem and quantum chaos.