Solitary wave propagation in media with step-like inhomogeneities

Mariya Lizunova; Oleksandr Gamayun

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arXiv · 2010.03385

Solitary wave propagation in media with step-like inhomogeneities

Mariya Lizunova·Oleksandr Gamayun

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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.

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Mariya Lizunova, Oleksandr Gamayun. 2020-10-07. Solitary wave propagation in media with step-like inhomogeneities. https://arxiv.org/abs/2010.03385

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