TY - JOUR
T1 - Collisions of counter-propagating pulses in coupled complex cubic-quintic Ginzburg-Landau equations
AU - Descalzi, O.
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
UR - http://www.scopus.com/inward/record.url?scp=34447513089&partnerID=8YFLogxK
U2 - 10.1140/epjst/e2007-00169-8
DO - 10.1140/epjst/e2007-00169-8
M3 - Article
AN - SCOPUS:34447513089
SN - 1951-6355
VL - 146
SP - 63
EP - 70
JO - European Physical Journal: Special Topics
JF - European Physical Journal: Special Topics
IS - 1
ER -