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Discrete dark solitons with multiple holes.

Hadi Susanto1, Magnus Johansson

  • 1Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands. h.susanto@math.utwente.nl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
Summary

Researchers studied dark solitons in a discrete nonlinear Schrödinger equation. They found stable intersite dark solitons with multiple holes, which disappear in a saddle-node bifurcation in the strong coupling limit.

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Area of Science:

  • Nonlinear Physics
  • Soliton Dynamics
  • Discrete Systems

Background:

  • The discrete nonlinear Schrödinger equation (DNLS) models various physical phenomena.
  • Dark solitons are stable localized waves in nonlinear systems.
  • Understanding soliton behavior in discrete lattices is crucial for applications.

Purpose of the Study:

  • To investigate staggered dark solitons in the focusing cubic DNLS.
  • To analyze dark solitons with multiple holes and their stability.
  • To explore the behavior of these solitons in the strong coupling limit and highly discrete cases.

Main Methods:

  • Numerical simulations of the discrete nonlinear Schrödinger equation.
  • Analysis of soliton solutions with varying numbers of holes.

Related Experiment Videos

  • Bifurcation analysis to identify stability limits.

    • Main Results:

    • Identified stable intersite dark solitons with multiple holes.
    • Demonstrated that these multi-hole dark solitons lack counterparts in the strong coupling limit.
    • Observed the disappearance of these structures via saddle-node bifurcations.
    • Studied the evolution and interaction of multi-hole solitons in a highly discrete regime.

    Conclusions:

    • Multi-hole dark solitons exhibit unique stable behaviors in discrete systems.
    • The strong coupling limit fundamentally alters the existence and stability of these complex soliton structures.
    • The DNLS provides a rich platform for exploring complex nonlinear wave phenomena.