Wave chaos in terms of normal modes

Wave propagation in a range-dependent waveguide can be considered as a clas sical physics problem similar to the quantum chaos problem situations. This analogy becomes especially strong when one uses the parabolic equation app roximation. By projecting the wave field taken in the quasiclassical approx imation onto eigenfunctions of the unperturbed boundary value problem, anal ytical description has been obtained for normal mode amplitudes in terms of geometrical optics relations. This approach provides a convenient way to s tudy how chaotic behavior of ray trajectories reveals itself in a range dep endence of mode amplitudes, and, hence, in the solution of the wave equatio n. An analog to nonlinear ray-medium resonance for normal modes has been in vestigated in details and the impact of this phenomenon on modal structure is discussed. It is argued that overlapping of different mode-medium resona nces causes a complicated range dependence of mode amplitude in almost the same manner as the overlapping of ray-medium resonances leads to ray chaos. [S1063-651X(99)05902-4].