TY - JOUR
T1 - Building patterns by traveling dipoles and vortices in two-dimensional periodic dissipative media
AU - Besse, V.
AU - Leblond, H.
AU - Mihalache, D.
AU - Malomed, B. A.
N1 - Funding Information:
The work of DM was supported in part by a Senior Chair Grant from the Région Pays de Loire, France . Support from the Romanian Ministry of Education and Research (Project PN-II-ID-PCE-2011-3-0083 ) is also acknowledged by this author.
PY - 2014/12/1
Y1 - 2014/12/1
N2 - We analyze pattern-formation scenarios in the two-dimensional (2D) complex Ginzburg-Landau (CGL) equation with the cubic-quintic (CQ) nonlinearity and a cellular potential. The equation models laser cavities with built-in gratings, which stabilize 2D patterns. The pattern-building process is initiated by kicking a compound mode, in the form of a dipole, quadrupole, or vortex which is composed of four local peaks. The hopping motion of the kicked mode through the cellular structure leads to the generation of various extended patterns pinned by the structure. In the ring-shaped system, the persisting freely moving dipole hits the stationary pattern from the opposite side, giving rise to several dynamical regimes, including periodic elastic collisions, i.e., persistent cycles of elastic collisions between the moving and quiescent dissipative solitons, and transient regimes featuring several collisions which end up by absorption of one soliton by the other. Still another noteworthy result is the transformation of a strongly kicked unstable vortex into a stably moving four-peaked cluster.
AB - We analyze pattern-formation scenarios in the two-dimensional (2D) complex Ginzburg-Landau (CGL) equation with the cubic-quintic (CQ) nonlinearity and a cellular potential. The equation models laser cavities with built-in gratings, which stabilize 2D patterns. The pattern-building process is initiated by kicking a compound mode, in the form of a dipole, quadrupole, or vortex which is composed of four local peaks. The hopping motion of the kicked mode through the cellular structure leads to the generation of various extended patterns pinned by the structure. In the ring-shaped system, the persisting freely moving dipole hits the stationary pattern from the opposite side, giving rise to several dynamical regimes, including periodic elastic collisions, i.e., persistent cycles of elastic collisions between the moving and quiescent dissipative solitons, and transient regimes featuring several collisions which end up by absorption of one soliton by the other. Still another noteworthy result is the transformation of a strongly kicked unstable vortex into a stably moving four-peaked cluster.
KW - Complex Ginzburg-Landau equation
KW - Dissipative soliton
KW - Nonlinear dynamics
KW - Pattern formation
KW - Spatial soliton
KW - Vortex
UR - http://www.scopus.com/inward/record.url?scp=84904968390&partnerID=8YFLogxK
U2 - 10.1016/j.optcom.2014.07.029
DO - 10.1016/j.optcom.2014.07.029
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AN - SCOPUS:84904968390
SN - 0030-4018
VL - 332
SP - 279
EP - 291
JO - Optics Communications
JF - Optics Communications
ER -