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

Orazio Descalzi; Helmut R. Brand; Jaime Cisternas

doi:10.1016/j.physa.2006.04.085

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

Orazio Descalzi, Helmut R. Brand, Jaime Cisternas

Grupo de Sistemas Complejos de Ingeniería

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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 language	American English
Pages (from-to)	41-45
Number of pages	5
Journal	Physica A: Statistical Mechanics and its Applications
Volume	371
Issue number	1
DOIs	https://doi.org/10.1016/j.physa.2006.04.085
State	Published - 1 Nov 2006

Keywords

Ginzburg-Landau equation
Hysteresis
Localized solutions

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title = "Hysteretic behavior of stable solutions at the onset of a weakly inverted instability",

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.",

keywords = "Ginzburg-Landau equation, Hysteresis, Localized solutions, Ginzburg-Landau equation, Hysteresis, Localized solutions",

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AU - Brand, Helmut R.

AU - Cisternas, Jaime

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N2 - 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.

AB - 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.

KW - Ginzburg-Landau equation

KW - Hysteresis

KW - Localized solutions

KW - Ginzburg-Landau equation

KW - Hysteresis

KW - Localized solutions

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