Hysteretic behavior of stable solutions at the onset of a weakly inverted instability

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Abstract

We investigate in the framework of the quintic complex Ginzburg-Landau (CGL) equation in one spatial dimension the dynamics of the transition from moving pulse solutions to moving hole solutions, a new class of solutions found for this equation very recently. We find that the transition between these two classes of solutions is weakly hysteretic and that the velocity of moving pulses and moving holes shows a jump across the transition, that is moving particles and moving holes travel at different speeds on both sides of the transition.

Original languageEnglish
Pages (from-to)41-45
Number of pages5
JournalPhysica A: Statistical Mechanics and its Applications
Volume371
Issue number1
DOIs
StatePublished - 1 Nov 2006

Bibliographical note

Funding Information:
The simulation software DimX developed at the laboratory INLN in France has been partially used for the numerical simulations. O.D. wishes to thank the support of FAI (Universidad de los Andes, 2006), FONDECYT (Project 1050660) and Project Anillo en Ciencia y Tecnología ACT 15. J.C. thanks FONDECYT (Project 1050660) for financial support.

Keywords

  • Ginzburg-Landau equation
  • Hysteresis
  • Localized solutions

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