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Stable Nonlinear Modes Sustained by Gauge Fields.

Yaroslav V Kartashov1, Vladimir V Konotop2

  • 1Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow 108840, Russia.

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|August 16, 2020
PubMed
Summary
This summary is machine-generated.

Gauge fields universally impact soliton dynamics in the nonlinear Schrödinger equation. Nonzero curvature enables stable localized states, even in repulsive or expulsive potentials, revealing new soliton behaviors.

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Area of Science:

  • Nonlinear optics
  • Quantum field theory
  • Mathematical physics

Background:

  • Solitons are stable, self-localized wave packets crucial in nonlinear systems.
  • Gauge fields introduce complexities in describing particle and wave behavior.
  • The nonlinear Schrödinger equation models various physical phenomena, including light propagation.

Purpose of the Study:

  • To investigate the universal effect of gauge fields on soliton dynamics.
  • To analyze the distinct roles of pure and non-pure gauge components.
  • To explore the conditions for stable soliton formation in multidimensional systems.

Main Methods:

  • Analysis of the two-dimensional spinor nonlinear Schrödinger equation.
  • Decomposition of the gauge field into pure and non-pure components.
  • Mathematical representation of soliton solutions as envelopes and carrier-mode states.

Main Results:

  • Gauge field components have differential effects on soliton localization and stability.
  • Curvature determines localization characteristics; pure gauge influences mode stability.
  • Nonzero curvature facilitates stable fundamental and vortex solitons in repulsive or expulsive media.

Conclusions:

  • Gauge fields are pivotal for controlling soliton existence, evolution, and stability.
  • Stable self-trapped states can emerge without external potentials due to gauge field-induced curvature.
  • This work expands the understanding of soliton behavior in complex nonlinear systems.