Acoustic pulse propagation in a non-ideal shallow-water waveguide

This study develops a theoretical framework for modeling acoustic pulse propagation in a non-ideal shallow-water waveguide. We derive an epsilon\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon $$\end{document}-pseudodifferential operator (epsilon\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon $$\end{document}-PDO) formulation from the general three-dimensional wave equation, that accounts for vertical stratification, bottom interaction, and slow horizontal inhomogeneity. Using the operator separation of variables method and the WKB-ansatz, we obtain single-mode equations describing the evolution of amplitude and phase along rays. The approach incorporates non-self-adjoint operators to model energy leakage through the bottom and introduces a Hamiltonian formalism for eikonal and transport equations, enabling the computation of amplitude, time, and phase fronts. Analytical and numerical examples are provided for different boundary conditions, including rigid, transparent, and partially reflecting interfaces. The results extend previous semiclassical and ray-based theories of wave propagation by including dissipative effects and improving the physical realism of shallow-water acoustic modeling.