Collisions of counter-propagating pulses in coupled complex cubic-quintic Ginzburg-Landau equations

O. Descalzi; J. Cisternas; P. Gutiérrez; H. R. Brand

doi:10.1140/epjst/e2007-00169-8

Collisions of counter-propagating pulses in coupled complex cubic-quintic Ginzburg-Landau equations

O. Descalzi^*, J. Cisternas, P. Gutiérrez, H. R. Brand

^*Corresponding author for this work

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

16 Scopus citations

Abstract

We discuss the results of the interaction ofcounter-propagating pulses for two coupled complex cubic-quintic Ginzburg-Landau equations as they arise near the onset of a weakly inverted Hopf bifurcation. As a result of the interaction of the pulses we find in 1D for periodic boundary conditions (corresponding to an annular geometry) many different possible outcomes. These are summarized in two phase diagrams using the approach velocity, v, and the real part of the cubiccross-coupling, c_r, of the counter-propagating waves asvariables while keeping all other parameters fixed. The novelphase diagram in the limit v → 0, c_r → 0 turns out to beparticularly rich and includes bound pairs of 2 π holes aswell as zigzag bound pairs of pulses.

Original language	English
Pages (from-to)	63-70
Number of pages	8
Journal	European Physical Journal: Special Topics
Volume	146
Issue number	1
DOIs	https://doi.org/10.1140/epjst/e2007-00169-8
State	Published - Jul 2007

Bibliographical note

Funding Information:
O.D. wishes to thank the support of FAI (Project No. ICIV-001-06, U. de los Andes), FONDECYT (Project No.1070098) and Project Anillo en Ciencia y Tecnología ACT15. J.C. thanks FONDECYT (Project No.1070098) for financial support. P.G. acknowledges support from Project Anillo en Ciencia y Tecnología ACT15. H.R.B. thanks the Deutsche Forschungsgemeinschaft for partial support of his work through Sonderforschungsbereich 481 ‘Polymere und Hybridmaterialien in inneren und äußeren Feldern’.

Keywords

Traveling-wave convection
Weakly inverted bifurcation
Reaction-diffusion system
Localized solutions
Subcritical instabilities
Solitons

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title = "Collisions of counter-propagating pulses in coupled complex cubic-quintic Ginzburg-Landau equations",

abstract = "We discuss the results of the interaction ofcounter-propagating pulses for two coupled complex cubic-quintic Ginzburg-Landau equations as they arise near the onset of a weakly inverted Hopf bifurcation. As a result of the interaction of the pulses we find in 1D for periodic boundary conditions (corresponding to an annular geometry) many different possible outcomes. These are summarized in two phase diagrams using the approach velocity, v, and the real part of the cubiccross-coupling, cr, of the counter-propagating waves asvariables while keeping all other parameters fixed. The novelphase diagram in the limit v → 0, cr → 0 turns out to beparticularly rich and includes bound pairs of 2 π holes aswell as zigzag bound pairs of pulses.",

keywords = "Traveling-wave convection, Weakly inverted bifurcation, Reaction-diffusion system, Localized solutions, Subcritical instabilities, Solitons",

author = "O. Descalzi and J. Cisternas and P. Guti{\'e}rrez and Brand, {H. R.}",

note = "Funding Information: O.D. wishes to thank the support of FAI (Project No. ICIV-001-06, U. de los Andes), FONDECYT (Project No.1070098) and Project Anillo en Ciencia y Tecnolog{\'i}a ACT15. J.C. thanks FONDECYT (Project No.1070098) for financial support. P.G. acknowledges support from Project Anillo en Ciencia y Tecnolog{\'i}a ACT15. H.R.B. thanks the Deutsche Forschungsgemeinschaft for partial support of his work through Sonderforschungsbereich 481 {\textquoteleft}Polymere und Hybridmaterialien in inneren und {\"a}u{\ss}eren Feldern{\textquoteright}.",

year = "2007",

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doi = "10.1140/epjst/e2007-00169-8",

language = "English",

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journal = "European Physical Journal: Special Topics",

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AU - Cisternas, J.

AU - Gutiérrez, P.

AU - Brand, H. R.

N1 - Funding Information: O.D. wishes to thank the support of FAI (Project No. ICIV-001-06, U. de los Andes), FONDECYT (Project No.1070098) and Project Anillo en Ciencia y Tecnología ACT15. J.C. thanks FONDECYT (Project No.1070098) for financial support. P.G. acknowledges support from Project Anillo en Ciencia y Tecnología ACT15. H.R.B. thanks the Deutsche Forschungsgemeinschaft for partial support of his work through Sonderforschungsbereich 481 ‘Polymere und Hybridmaterialien in inneren und äußeren Feldern’.

PY - 2007/7

Y1 - 2007/7

N2 - We discuss the results of the interaction ofcounter-propagating pulses for two coupled complex cubic-quintic Ginzburg-Landau equations as they arise near the onset of a weakly inverted Hopf bifurcation. As a result of the interaction of the pulses we find in 1D for periodic boundary conditions (corresponding to an annular geometry) many different possible outcomes. These are summarized in two phase diagrams using the approach velocity, v, and the real part of the cubiccross-coupling, cr, of the counter-propagating waves asvariables while keeping all other parameters fixed. The novelphase diagram in the limit v → 0, cr → 0 turns out to beparticularly rich and includes bound pairs of 2 π holes aswell as zigzag bound pairs of pulses.

AB - We discuss the results of the interaction ofcounter-propagating pulses for two coupled complex cubic-quintic Ginzburg-Landau equations as they arise near the onset of a weakly inverted Hopf bifurcation. As a result of the interaction of the pulses we find in 1D for periodic boundary conditions (corresponding to an annular geometry) many different possible outcomes. These are summarized in two phase diagrams using the approach velocity, v, and the real part of the cubiccross-coupling, cr, of the counter-propagating waves asvariables while keeping all other parameters fixed. The novelphase diagram in the limit v → 0, cr → 0 turns out to beparticularly rich and includes bound pairs of 2 π holes aswell as zigzag bound pairs of pulses.

KW - Traveling-wave convection

KW - Weakly inverted bifurcation

KW - Reaction-diffusion system

KW - Localized solutions

KW - Subcritical instabilities

KW - Solitons

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DO - 10.1140/epjst/e2007-00169-8

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SN - 1951-6355

VL - 146

SP - 63

EP - 70

JO - European Physical Journal: Special Topics

JF - European Physical Journal: Special Topics

IS - 1

ER -

Collisions of counter-propagating pulses in coupled complex cubic-quintic Ginzburg-Landau equations

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Keywords

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