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Solitary wave billiards.

Jesús Cuevas-Maraver1, Panayotis G Kevrekidis2, Hong-Kun Zhang2

  • 1Grupo de Física No Lineal, Departamento de Física Aplicada I, Universidad de Sevilla, Escuela Politécnica Superior, Calle Virgen de Africa 7, 41011 Sevilla, Spain and Instituto de Matemáticas de la Universidad de Sevilla (IMUS), Edificio Celestino Mutis, Avenida Reina Mercedes s/n, 41012 Sevilla, Spain.

Physical Review. E
|April 19, 2023
PubMed
Summary
This summary is machine-generated.

Solitary wave billiards are generally chaotic, even when classical particle billiards are integrable. The chaoticity depends on wave speed and potential properties, with a negative Goos-Hänchen effect causing trajectory shifts and domain shrinkage.

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Area of Science:

  • Nonlinear dynamics
  • Wave phenomena
  • Mathematical physics

Background:

  • Billiard systems are classical models for chaotic dynamics.
  • Solitary waves are localized wave packets that maintain their shape.
  • Understanding wave behavior in confined systems is crucial for various physics fields.

Purpose of the Study:

  • To investigate the dynamics of solitary waves in billiard systems.
  • To compare the behavior of solitary wave billiards with classical particle billiards.
  • To determine the factors influencing the chaoticity of solitary wave billiards.

Main Methods:

  • Simulating solitary wave collisions with boundaries in enclosed regions.
  • Analyzing trajectories in both integrable and chaotic classical billiard scenarios.
  • Investigating the role of wave speed and potential properties on scattering.

Main Results:

  • Solitary wave billiards exhibit chaotic behavior even in classically integrable systems.
  • The degree of chaoticity is influenced by solitary wave speed and potential characteristics.
  • A negative Goos-Hänchen effect contributes to trajectory shifts and effective domain shrinkage.

Conclusions:

  • Solitary wave billiards present a distinct dynamical system compared to particle billiards.
  • The findings highlight the complex interplay between wave properties and boundary interactions.
  • The negative Goos-Hänchen effect offers a new perspective on wave scattering in confined geometries.