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Methods for discrete solitons in nonlinear lattices.

Mark J Ablowitz1, Ziad H Musslimani, Gino Biondini

  • 1Department of Applied Mathematics, University of Colorado, Campus Box 526, Boulder, Colorado 80309-0526, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
PubMed
Summary

A new method identifies discrete solitons in nonlinear lattices, like optical waveguide arrays. This research provides formulas for soliton shapes and velocities in specific conditions.

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Area of Science:

  • Nonlinear optics
  • Condensed matter physics
  • Wave phenomena

Background:

  • Nonlinear lattices support complex wave phenomena, including solitons.
  • Understanding discrete solitons is crucial for applications in optics and materials science.
  • Previous methods often relied on continuous approximations, limiting accuracy for discrete systems.

Purpose of the Study:

  • To introduce a novel method for finding discrete solitons in nonlinear lattices.
  • To investigate both stationary and traveling-wave solitons.
  • To apply the method to nonlinear optical waveguide arrays as a prototype.

Main Methods:

  • Development of a discrete analytical method.
  • Perturbative analysis in the limit of small wave velocity.

Related Experiment Videos

  • Derivation of formulas for soliton mode shapes and velocity.

    • Main Results:

    • Successful identification of discrete solitons.
    • Formulas derived for mode shapes and velocity of stationary and traveling-wave solitons.
    • Validation using nonlinear optical waveguide arrays.

    Conclusions:

    • The introduced method effectively finds discrete solitons in nonlinear lattices.
    • The derived formulas offer accurate predictions for soliton properties in specific regimes.
    • This work advances the understanding and prediction of soliton dynamics in discrete systems.