Nonlinear responses from the interaction of two progressing waves at an interface

TL;DR

This paper investigates how two interacting nonlinear waves at an interface generate new waves and reveal properties of the media, including interface location and nonlinear characteristics, through analysis of scalar semilinear wave equations.

Contribution

It provides a mathematical analysis of wave interactions at media interfaces, showing how nonlinear responses can be used to infer media properties and interface discontinuities.

Findings

New wave generation from nonlinear interactions

Interface location can be determined from wave data

Magnitude of jump discontinuity can be identified

Abstract

For scalar semilinear wave equations, we analyze the interaction of two (distorted) plane waves at an interface between media of different nonlinear properties. We show that new waves are generated from the nonlinear interactions, which might be responsible for the observed nonlinear effects in applications. Also, we show that the incident waves and the nonlinear responses determine the location of the interface and some information of the nonlinear properties of the media. In particular, for the case of a jump discontinuity at the interface, we can determine the magnitude of the jump.