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

^*Corresponding author for this work

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	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

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

Access to Document

10.1016/j.physa.2006.04.085

Cite this

@article{5b9ebd42aaf14c9cb770df0455be11cb,

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",

author = "Orazio Descalzi and Brand, {Helmut R.} and Jaime Cisternas",

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 Tecnolog{\'i}a ACT 15. J.C. thanks FONDECYT (Project 1050660) for financial support.",

year = "2006",

month = nov,

day = "1",

doi = "10.1016/j.physa.2006.04.085",

language = "English",

volume = "371",

pages = "41--45",

journal = "Physica A: Statistical Mechanics and its Applications",

issn = "0378-4371",

publisher = "Elsevier",

number = "1",

}

TY - JOUR

T1 - Hysteretic behavior of stable solutions at the onset of a weakly inverted instability

AU - Descalzi, Orazio

AU - Brand, Helmut R.

AU - Cisternas, Jaime

N1 - 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.

PY - 2006/11/1

Y1 - 2006/11/1

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

UR - http://www.scopus.com/inward/record.url?scp=33748084048&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2006.04.085

DO - 10.1016/j.physa.2006.04.085

M3 - Article

AN - SCOPUS:33748084048

SN - 0378-4371

VL - 371

SP - 41

EP - 45

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1

ER -

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

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this