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Related Experiment Videos

Translationally invariant discrete kinks from one-dimensional maps.

I V Barashenkov1, O F Oxtoby, Dmitry E Pelinovsky

  • 1Department of Mathematics, University of Cape Town, Rondebosch 7701, South Africa.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
Summary

Researchers explored discretizations of the phi4 theory, finding new ways to center stationary kinks. This work reveals an underlying map enabling kinks to be positioned anywhere between lattice sites.

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Area of Science:

  • Theoretical Physics
  • Computational Physics
  • Mathematical Physics

Background:

  • Stationary kinks in phi4 theory discretizations typically localize at specific lattice positions.
  • This localization limits the flexibility and applicability of kink solutions in discrete systems.

Purpose of the Study:

  • To identify novel discretizations of the phi4 theory that permit stationary kinks to be centered at arbitrary positions.
  • To explore the implications of translational invariance for kink solutions in discrete systems.

Main Methods:

  • Investigated discretizations of the phi4 theory beyond standard lattice site or inter-site centering.
  • Derived the condition for translational invariance of stationary kinks, revealing an underlying one-dimensional map.
  • Developed a constructive algorithm based on this map to generate exceptional discretizations.

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Main Results:

  • Demonstrated that translational invariance of stationary kinks is linked to an underlying map of the form phi(n+1) =F (phi(n)).
  • Generated three distinct families of exceptional discretizations that allow for arbitrary kink centering.
  • These discretizations overcome the usual limitations of kink localization in discrete phi4 models.

Conclusions:

  • Exceptional discretizations enabling arbitrary kink centering in phi4 theory are achievable.
  • The identified one-dimensional map provides a theoretical framework and practical tool for constructing such discretizations.
  • This research expands the possibilities for utilizing kink solutions in discrete physical models.