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Internal modes in sine-Gordon chain.

Jaroslaw E Prilepsky1, Alexander S Kovalev

  • 1B. Verkin Institute for Low Temperature Physics and Engineering, NASU, 47 Lenin Ave., Kharkov 61103, Ukraine.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2005
PubMed
Summary

We studied internal modes in a discrete sine-Gordon equation. Our findings explain how frequency dependence detaches from the spectrum due to discreteness, impacting kink behavior.

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Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Mathematical physics

Background:

  • Stable kinks in discrete systems exhibit complex internal modes.
  • The behavior of these modes is sensitive to system parameters like discreteness.

Purpose of the Study:

  • To investigate the detachment of antisymmetric internal mode frequency dependence from the spectrum.
  • To understand the influence of discreteness and system size on mode frequencies.
  • To explain the origin of spectral peculiarities in discrete sine-Gordon models.

Main Methods:

  • Analysis of lowest mode frequencies as a function of the number of sites.
  • Analysis of mode frequencies as a function of the discreteness parameter.
  • Development of a simplified analytical approach.

Main Results:

  • The frequency dependence of the antisymmetric internal mode detaches from the spectrum.
  • This detachment is linked to specific values of the intersite coupling parameter.
  • Spectral peculiarities arise from this frequency dependence detachment.

Conclusions:

  • The study elucidates the mechanism behind spectral peculiarities in discrete sine-Gordon kinks.
  • Understanding these internal modes is crucial for discrete nonlinear systems.
  • The simplified approach provides insights into the behavior of discrete solitons.

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