Summary: Physics Letters A 343 (2005) 417422
Bifurcations from stationary to pulsating solitons
in the cubicquintic complex GinzburgLandau equation
Eduard N. Tsoy ,1
, Nail Akhmediev
Optical Sciences Group, Research School of Physical Sciences and Engineering, The Australian National University,
Canberra, ACT 0200, Australia
Received 4 May 2005; accepted 10 May 2005
Available online 1 July 2005
Communicated by V.M. Agranovich
Stationary to pulsating soliton bifurcation analysis of the complex GinzburgLandau 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.
2005 Elsevier B.V. All rights reserved.
PACS: 04.30.Nk; 05.45.Yv; 42.65.Sf; 42.65.Tg