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Dynamical models for dissipative localized waves of the complex Ginzburg-Landau equation Eduard N. Tsoy
 

Summary: Dynamical models for dissipative localized waves of the complex Ginzburg-Landau equation
Eduard N. Tsoy
Physical-Technical Institute of the Uzbek Academy of Sciences, Mavlyanov street, 2-B, Tashkent, 700084, Uzbekistan
Adrian Ankiewicz and Nail Akhmediev
Optical Sciences Group, Research School of Physical Sciences and Engineering, The Australian National University,
Canberra, Australian Capital Territory 0200, Australia
Received 2 November 2005; published 29 March 2006
Finite-dimensional dynamical models for solitons of the cubic-quintic complex Ginzburg-Landau equation
CGLE are derived. The models describe the evolution of the pulse parameters, such as the maximum
amplitude, pulse width, and chirp. A clear correspondence between attractors of the finite-dimensional dynami-
cal systems and localized waves of the continuous dissipative system is demonstrated. It is shown that station-
ary solitons of the CGLE correspond to fixed points, while pulsating solitons are associated with stable limit
cycles. The models show that a transformation from a stationary soliton to a pulsating soliton is the result of
a Hopf bifurcation in the reduced dynamical system. The appearance of moving fronts kinks in the CGLE is
related to the loss of stability of the limit cycles. Bifurcation boundaries and pulse behavior in the regions
between the boundaries, for a wide range of system parameters, are found from analysis of the reduced
dynamical models. We also provide a comparison between various models and their correspondence to the
exact results.
DOI: 10.1103/PhysRevE.73.036621 PACS number s : 05.45.Yv, 04.30.Nk, 42.65.Sf, 42.65.Tg
I. INTRODUCTION

  

Source: Akhmediev, Nail - Research School of Physical Sciences and Engineering, Australian National University
Australian National University, Research School of Physical Sciences and Engineering, Optical Sciences Group

 

Collections: Engineering; Physics