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 -