Solitary wave propagation in media with step-like inhomogeneities

TL;DR

This paper investigates how solitary waves behave when passing through media with abrupt changes in properties, revealing model-independent velocity predictions akin to a hyperbolic Snell's law.

Contribution

It introduces a unified approach to analyze solitary wave propagation across step-like inhomogeneities in different models and protocols.

Findings

Solitary waves retain their shape due to topological protection.

Final velocity predictions are model-independent.

The results resemble a hyperbolic Snell's law for wave refraction.

Abstract

We consider the wave propagation in media with step-like inhomogeneities. We choose two different protocols: (I) a step-like spatial dependence of the coupling constant that physically corresponds to the junction of two systems and (II) the step-like time-dependence of the coupling constant that corresponds to a quench protocol. In both scenarios, we study the propagation of the solitary wave in $\varphi^4$ and the sine-Gordon model. Due to topological protection, the solitary wave retains its form. This allows us to give model-independent predictions about its final velocity, which can be interpreted as the "hyperbolic" Snell's law.