TY - JOUR
T1 - Bifurcations from stationary to pulsating solitons in the cubic-quintic complex Ginzburg-Landau equation
AU - Tsoy, Eduard N.
AU - Akhmediev, Nail
PY - 2005/8/22
Y1 - 2005/8/22
N2 - Stationary to pulsating soliton bifurcation analysis of the complex Ginzburg-Landau equation (CGLE) is presented. The analysis is based on a reduction from an infinite-dimensional dynamical dissipative system to a finite-dimensional model. Stationary solitons, with constant amplitude and width, are associated with fixed points in the model. For the first time, pulsating solitons are shown to be stable limit cycles in the finite-dimensional dynamical system. The boundaries between the two types of solutions are obtained approximately from the reduced model. These boundaries are reasonably close to those predicted by direct numerical simulations of the CGLE.
AB - Stationary to pulsating soliton bifurcation analysis of the complex Ginzburg-Landau equation (CGLE) is presented. The analysis is based on a reduction from an infinite-dimensional dynamical dissipative system to a finite-dimensional model. Stationary solitons, with constant amplitude and width, are associated with fixed points in the model. For the first time, pulsating solitons are shown to be stable limit cycles in the finite-dimensional dynamical system. The boundaries between the two types of solutions are obtained approximately from the reduced model. These boundaries are reasonably close to those predicted by direct numerical simulations of the CGLE.
UR - http://www.scopus.com/inward/record.url?scp=23144463877&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2005.05.102
DO - 10.1016/j.physleta.2005.05.102
M3 - Article
SN - 0375-9601
VL - 343
SP - 417
EP - 422
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 6
ER -