Asymptotic solution for the problem of sound propagation in a sea with an underwater canyon

The problem of the sound propagation in shallow-water waveguide with a seabottom featuring canyon-type inhomogeneity of a specific form is considered. The sound pressure in such waveguide is represented in a form of modal expansion and the equations for modal coefficients are derived. In case of a single-mode adiabatic propagation, it is possible to neglect the mode interaction and omit the coupling terms in these equations. The uncoupled equation for the mode amplitude admits an explicit analytical solution via the separation of variables.