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Convective instability induced by two-points nonlocality.

Roberta Zambrini1, Francesco Papoff

  • 1SUPA, Department of Physics, University of Strathclyde, 107 Rottenrow, Glasgow G4 0NG, UK.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
PubMed
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Nonlocal coupling in diffusive nonlinear systems creates unique instabilities and opposite phase/group velocities, differing from drift-induced effects. Theoretical predictions align with numerical results, explaining complex dynamics in these systems.

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Optical Systems

Background:

  • Diffusive nonlinear systems are crucial in various scientific fields.
  • Nonlocal coupling, often from optical feedback misalignment, introduces complex behaviors.
  • Existing stability analyses may not fully capture nonlocal effects.

Purpose of the Study:

  • To extend stability analysis for diffusive nonlinear systems with nonlocal coupling.
  • To identify convective and absolute instability thresholds.
  • To understand the unique dynamics introduced by nonlocality.

Main Methods:

  • Expanded stability analysis based on previous work (Papoff & Zambrini, 2005).
  • Investigated systems with saturable nonlinearity.
  • Employed numerical simulations to validate theoretical predictions.

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Main Results:

  • Nonlocality leads to distinct effects compared to drift-dominated systems.
  • Observed opposite phase and group velocities for certain modes.
  • Identified a specific instability region due to nonlocality.
  • Theoretical predictions showed strong agreement with numerical results.

Conclusions:

  • The study provides a comprehensive stability analysis for nonlocal diffusive nonlinear systems.
  • Understanding the stability diagram is key to interpreting complex dynamics.
  • Nonlocality significantly alters system behavior, impacting phase and group velocities and introducing instability regions.