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Summary: Interrelation between various branches of stable solitons
in dissipative systems±±conjecture for stability criterion
J.M. Soto-Crespo a,*, N. Akhmediev b
, G. Town c
a
Instituto de Optica, CSIC, Serrano 121, 28006 Madrid, Spain
b
Australian Photonics CRC, Optical Science Centre, Research School of Physics Science and Engineering,
Australian National University, Canberra, ACT 0200, Australia
c
School of Electrical and Information Engineering (J03), University of Sydney, Sydney, NSW 2006, Australia
Received 7 June 2001; received in revised form 28 August 2001; accepted 3 October 2001
Abstract
We show that the complex cubic-quintic Ginzburg±Landau equation has a multiplicity of soliton solutions for the
same set of equation parameters. They can either be stable or unstable. We show that the branches of stable solitons can
be interrelated, i.e. stable solitons of one branch can be transformed into stable solitons of another branch when the
parameters of the system are changed. This connection occurs via some branches of unstable solutions. The trans-
formation occurs at the points of bifurcation. Based on these results, we propose a conjecture for a stability criterion for
solitons in dissipative systems. Ó 2001 Elsevier Science B.V. All rights reserved.
Keywords: Soliton; Passively mode-locked lasers; Ginzburg±Landau equation; Stability criterion
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