# An adiabatic mode time-dependent parabolic equation

## TL;DR

This paper derives a new adiabatic mode time-dependent parabolic equation for 3D underwater acoustic propagation using the multiple-scale method, providing a basis for analyzing complex acoustic environments.

## Contribution

It introduces a novel derivation of the adiabatic mode equation for 3D underwater acoustics via the multiple-scale approach.

## Key findings

- Formulation of the adiabatic mode time-dependent parabolic equation
- Analysis of the Cauchy problem for the derived equation
- Potential applications in underwater acoustic modeling

## Abstract

An adiabatic mode time-dependent parabolic equation for the 3D problems of underwater acoustic propagation problem is derived by the multiple-scale method. The Cauchy problem for this equation is considered.