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Creeping solitons in dissipative systems and their bifurcations Wonkeun Chang, Adrian Ankiewicz, and Nail Akhmediev
 

Summary: Creeping solitons in dissipative systems and their bifurcations
Wonkeun Chang, Adrian Ankiewicz, and Nail Akhmediev
Optical Sciences Group, Research School of Physical Sciences and Engineering, The Australian National University,
Canberra, ACT 0200, Australia
J. M. Soto-Crespo
Instituto de Óptica, CSIC, Serrano 121, 28006 Madrid, Spain
Received 13 April 2007; published 26 July 2007
We present a detailed numerical study of creeping solitons in dissipative systems. A bifurcation diagram has
been constructed for the region of transition between solitons and fronts. It shows a rich variety of transitions
between various types of localized solutions. For the first time, we have found a sequence of period-doubling
bifurcations of creeping solitons, and also a symmetry-breaking instability of creeping solitons. Creeping
solitons may involve many frequencies in their dynamics, and this can result, in particular, in a multiplicity of
zig-zag motions.
DOI: 10.1103/PhysRevE.76.016607 PACS number s : 05.45.Yv, 42.65.Tg, 47.20.Ky
I. INTRODUCTION
In general, nonlinear dissipative systems possess station-
ary and moving localized solutions. For a given set of equa-
tion parameters, the form of the solution is usually set, so
only one exists for a specified situation. Occasionally there
can be a few, but we do not have a family of them. Dissipa-

  

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