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Physics Letters A 317 (2003) 287292 www.elsevier.com/locate/pla

Summary: Physics Letters A 317 (2003) 287≠292
Exploding solitons and Shil'nikov's theorem
Nail Akhmediev a
, J.M. Soto-Crespo b
a Optical Sciences Centre, Research School of Physical Sciences and Engineering, The Australian National University,
Canberra ACT 0200, Australia
b Instituto de ”ptica, C.S.I.C., Serrano 121, 28006 Madrid, Spain
Received 13 August 2003; accepted 17 August 2003
Communicated by V.M. Agranovich
We have performed a detailed linear stability analysis of exploding solitons of the complex cubic≠quintic Ginzburg≠Landau
(CGLE) equation. We have found, numerically, the whole set of perturbation eigenvalues for these solitons. We propose a
scenario of soliton evolution based on this spectrum of eigenvalues. We relate exploding and self-restoring behavior of solitons
to the Shil'nikov theorem, and point out common features and differences between our system, with an infinite number of
degrees of freedom, and Shil'nikov's system with three degrees of freedom.
2003 Elsevier B.V. All rights reserved.
PACS: 42.65.-k; 47.20.Ky; 47.25.Qv
Keywords: Dissipative solitons; Complex Ginzburg≠Landau equation
Exploding solitons were recently found in numeri-


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