SOLUTIONS OF THE HELMHOLTZ EQUATION CONCENTRATED NEAR THE AXIS OF A DEEP-WATER WAVEGUIDE IN A RANGE-DEPENDENT MEDIUM

This paper examines a two-dimensional deep-water waveguide in a range-dependent medium. Solutions of the homogeneous Helmholtz equation concentrated near the waveguide axis and which decrease exponentially outside a strip containing the axis are constructed. These solutions have the form of exponentials multiplied by parabolic cylinder functions whose arguments are an infinite series in powers of ω-1/2, where ω is a cyclic frequency. Coefficients of these series are found from a recurrent system of differential equations up to terms allowing to get a residual (difference between the left-hand side of the Helmholtz equation and zero) of order ω-1/2. Arbitrary constants of general solutions of arising differential equations are calculated going over to the limiting case of a range-independent medium. Numerical simulations are carried out for a deterministic model of a range-dependent ocean, where the range-dependence results for change in geographic location. Parameters of this medium model are matched with the AET experiment.