The nonlinear behavior of acoustic rays in underwater sound channels is examined using a set of parabolic ray equations. Two sound speed profiles, a Munk canonical and a double-duct profile, are investigated. For range-independent but stratified ocean sound speed profiles, analytical results concerning the sound ray trajectory and wave length are obtained. The stability of the system is found to be marginal stable, which leads to the phenomenon of wave front folding. Next, a perturbed system attributed to a single-mode internal wave is examined. The stability, bifurcation and other nonlinear dynamic issues of the nearly integrable system are explored using a combination of phase plane trajectories, Poincar6 maps, bifurcation diagrams, Lyapunov exponents and Floquet multipliers. ~) 1998 Elsevier Science Ltd. All rights reserved
1. Introduction
In this paper, we look into the nonlinear dynamic issues of acoustic ray propagation in deep-water sound channels in order to improve the understanding of the governing mechanisms for long-range propagation problems. This is to examine theoretical means of extending ranges of propagated signals and improve the process of their recognition. Two model sound speed profiles, namely a canonical Munk profile and a double-duct profile, are considered. The dynamic phenomena associated with these profiles are analogous to a single-well and a double-well potential problems. If the internal wave perturbation is ignored, the resultant is an autonomous, Hamiltonian system, for which a close form solution can be obtained. Phase plane ray trajectories, ray crossing range, and crossing time can also be analytically determined. The stability of this system is identified as marginally