Solitary wave billiards

TL;DR

This paper investigates the dynamics of solitary wave billiards, revealing that solitary waves generally exhibit chaotic trajectories even in geometries where classical particles follow predictable paths, influenced by wave deformation and boundary interactions.

Contribution

It introduces the concept of solitary wave billiards and demonstrates their predominantly chaotic behavior, contrasting with classical particle billiards, and analyzes the effects of wave deformation and boundary scattering.

Findings

Solitary wave billiards are generally chaotic.

Chaoticity depends on wave speed and potential properties.

Negative Goos-H"anchen effect influences wave scattering and domain size.

Abstract

In the present work we explore the concept of solitary wave billiards. I.e., instead of a point particle, we examine a solitary wave in an enclosed region and explore its collision with the boundaries and the resulting trajectories in cases which for particle billiards are known to be integrable and for cases that are known to be chaotic. A principal conclusion is that solitary wave billiards are generically found to be chaotic even in cases where the classical particle billiards are integrable. However, the degree of resulting chaoticity depends on the particle speed and on the properties of the potential. Furthermore, the nature of the scattering of the deformable solitary wave particle is elucidated on the basis of a negative Goos-H\"anchen effect which, in addition to a trajectory shift, also results in an effective shrinkage of the billiard domain.