The nonlinear and stochastic dynamics of rays in regular transversely inhomogeneous media

A new method is proposed for analyzing the dynamics of rays in waveguide media in which the cross section is of arbitrary shape. The method is based on ideas relating to the existence and destruction of invariant tori in the Hamiltonian mechanics of particles. The main feature of the method is the absence of any reference to a system of coordinates with separable variables. Phenomena of nonlinear resonance between various degrees of freedom of a ray are considered, along with the stochastization of the ray owing to the interaction of the resonances. Limits are established for the transverse dimensions of the waveguide channel and for the distance that the wave front can propagate without significant distortion.