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Related Experiment Videos

Stable embedded solitons.

Jianke Yang1

  • 1Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401, USA.

Physical Review Letters
|November 13, 2003
PubMed
Summary
This summary is machine-generated.

Stable embedded solitons were discovered in nonlinear optics, challenging previous assumptions. These robust solitons, described by the nonlinear Schrödinger equation, are stable even when interacting with the linear spectrum.

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Area of Science:

  • Nonlinear optics
  • Mathematical physics

Background:

  • Embedded solitons are typically considered unstable.
  • Previous research suggested resonance with the linear spectrum leads to instability.

Purpose of the Study:

  • To investigate the existence and stability of embedded solitons in the generalized third-order nonlinear Schrödinger equation.
  • To challenge the prevailing understanding of embedded soliton stability.

Main Methods:

  • Reduction of the generalized third-order nonlinear Schrödinger equation to a perturbed complex modified Korteweg-de Vries equation.
  • Development of a soliton perturbation theory.
  • Numerical simulations to validate analytical findings.

Main Results:

  • Discovery of a continuous family of stable, sech-shaped embedded solitons.

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  • Demonstration of nonlinear stability for these solitons.
  • Confirmation that embedded solitons can be robust despite resonance with the linear spectrum.

    • Conclusions:

    • Embedded solitons can exhibit remarkable stability, contrary to prior expectations.
    • The findings broaden the understanding of soliton dynamics in nonlinear systems.
    • This research opens new avenues for exploring stable nonlinear wave phenomena.