Sources and sinks in the vicinity of a weakly inverted instability

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Abstract

The dynamics of perturbations around sinks and sources of traveling waves (TW) is studied in the cubic-quintic Ginzburg-Landau equation from an analytical point of view. Perturbations generically propagate in a direction opposite to the TW. Thus, a sink of TW is a source of perturbations and vice versa. For small values of time we predict there is a lower bound for the group velocity. For large values of time we predict the asymptotic value of the group velocity of the wave packet. Both predictions are in good agreement with direct numerical simulations.
Original languageAmerican English
Pages (from-to)2821-2826
Number of pages6
JournalInternational Journal of Bifurcation and Chaos
Volume17
Issue number8
DOIs
StatePublished - 1 Jan 2007

Keywords

  • Cubic-quintic Ginzburg-Landau equation
  • Dissipative dark solitons
  • Sinks
  • Sources

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