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Linear stability analysis of walking vector solitons.

D Mihalache1, D Mazilu, L C Crasovan

  • 1Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering, Institute of Atomic Physics, P.O. Box MG-6, Bucharest, Romania.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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Linear stability analysis reveals complex eigenvalue behavior in walking vector solitons of nonlinear Schrödinger equations, leading to intricate instability patterns. Certain soliton types demonstrate dynamic stability across parameter variations.

Area of Science:

  • Nonlinear Optics
  • Mathematical Physics
  • Soliton Dynamics

Background:

  • Coupled nonlinear Schrödinger equations model various physical phenomena.
  • Vector solitons are complex solutions exhibiting particle-like behavior.
  • Linear stability analysis is crucial for understanding soliton dynamics.

Purpose of the Study:

  • To perform a linear stability analysis of two-parameter families of walking vector solitons.
  • To investigate the nature of eigenvalues in the linearized problem.
  • To characterize the instability regions for lowest-order soliton types.

Main Methods:

  • Linear stability analysis of vector solitons.
  • Examination of eigenvalues in the parameter space.
  • Identification of critical points and bifurcation scenarios.

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Main Results:

  • Eigenvalues can be complex-valued, influencing stability.
  • Instability patterns arise from complex Lyapunov eigenvalues.
  • Two main scenarios for eigenvalue behavior at critical points were identified: transition to real eigenvalues and complexification via bifurcation.

Conclusions:

  • All known lowest-order soliton types (slow, fast, in-phase, out-of-phase) exhibit dynamic stability in specific parameter regions.
  • The complex eigenvalue behavior dictates intricate instability patterns.
  • Understanding these stability regions is vital for controlling soliton propagation.