Nonlinear acoustic waves in channels with variable cross sections

TL;DR

This paper investigates the symmetry properties of nonlinear acoustic wave equations in channels with variable cross sections, deriving invariant and approximate solutions for specific channel profiles.

Contribution

It identifies conditions under which the symmetry group extends and provides new invariant and approximate solutions for nonlinear acoustic waves in variable cross section channels.

Findings

Extended symmetry groups for certain cross section profiles

Invariant solutions for specific channel geometries

Approximate solutions for smoothly varying cross sections

Abstract

The point symmetry group is studied for the generalized Webster-type equation describing non-linear acoustic waves in lossy channels with variable cross sections. It is shown that, for certain types of cross section profiles, the admitted symmetry group is extended and the invariant solutions corresponding to these profiles are obtained. Approximate analytic solutions to the generalized Webster equation are derived for channels with smoothly varying cross sections and arbitrary initial conditions.