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arXiv · 2511.09257

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

Aleksandr Kaplun·Boris Katsnelson
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Abstract

This study develops a theoretical framework for modeling acoustic pulse propagation in a non-ideal shallow-water waveguide. We derive an {\epsilon}-pseudodifferential operator ({\epsilon}-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 Neumann (ideal), self-adjoint, 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.

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Aleksandr Kaplun, Boris Katsnelson. 2025-11-12. Acoustic pulse propagation in a non-ideal shallow-water model. https://arxiv.org/abs/2511.09257

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