Transition from pulses to fronts in the cubic-quintic complex Ginzburg-Landau equation

Pablo Gutiérrez, Daniel Escaff, Orazio Descalzi

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The cubic-quintic complex Ginzburg-Landau is the amplitude equation for systems in the vicinity of an oscillatory sub-critical bifurcation (Andronov-Hopf), and it shows different localized structures. For pulse-type localized structures, we review an approximation scheme that enables us to compute some properties of the structures, like their existence range. From that scheme, we obtain conditions for the existence of pulses in the upper limit of a control parameter. When we study the width of pulses in that limit, the analytical expression shows that it is related to the transition between pulses and fronts.This fact is consistent with numerical simulations.
Original languageAmerican English
Pages (from-to)3227-3238
Number of pages12
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume367
Issue number1901
DOIs
StatePublished - 28 Aug 2009

Keywords

  • Bifurcations
  • Ginzburg-Landau equation
  • Localized structures

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