On the resonant reflection of weak, nonlinear sound waves off an entropy wave

TL;DR

This paper derives a specialized Schrödinger equation to model how weak, nonlinear sound waves resonate and reflect off entropy waves with a sawtooth pattern.

Contribution

It introduces a new mathematical model specifically for the resonant reflection of weak nonlinear sound waves off entropy waves.

Findings

Derivation of a degenerate quasilinear Schrödinger equation

Model captures resonant reflection phenomena

Provides a foundation for further analytical and numerical studies

Abstract

We derive a degenerate quasilinear Schr\"odinger equation that describes the resonant reflection of very weak, nonlinear sound waves off a weak sawtooth entropy wave.