Bifurcation structure of dissipative solitons

Damia Gomila, A. J. Scroggie, W. J. Firth

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

In this paper we analyze in detail the structure of the phase space of a reversible dynamical system describing the stationary solutions of a model for a nonlinear optical cavity. We compare our results with the general picture described in [P.D. Woods, A.R. Champneys, Physica D 129 (1999) 147; P. Coullet, C. Riera, C. Tresser, Phys. Rev. Lett. 84 (2000) 3069] and find that the stable and unstable manifolds of homogeneous and patterned solutions present a much higher level of complexity than predicted, including the existence of additional localized solutions and fronts. This extra complexity arises due to homoclinic and heteroclinic intersections of the invariant manifolds of low-amplitude periodic solutions, and to the fact that these periodic solutions together with the high-amplitude ones constitute a one-parameter family generating a closed line on the symmetry plane. (c) 2006 Elsevier B.V. All rights reserved.

LanguageEnglish
Pages70-77
Number of pages8
JournalPhysica D: Nonlinear Phenomena
Volume227
Issue number1
DOIs
Publication statusPublished - 1 Mar 2007

Fingerprint

solitary waves
dynamical systems
intersections
cavities
symmetry

Keywords

  • homoclinic bifurcations
  • localized structures
  • dissipative solitons
  • reversible systems
  • dynamical systems
  • passive optical susyems

Cite this

Gomila, Damia ; Scroggie, A. J. ; Firth, W. J. / Bifurcation structure of dissipative solitons. In: Physica D: Nonlinear Phenomena. 2007 ; Vol. 227, No. 1. pp. 70-77.
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Bifurcation structure of dissipative solitons. / Gomila, Damia; Scroggie, A. J.; Firth, W. J.

In: Physica D: Nonlinear Phenomena, Vol. 227, No. 1, 01.03.2007, p. 70-77.

Research output: Contribution to journalArticle

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AU - Scroggie, A. J.

AU - Firth, W. J.

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AB - In this paper we analyze in detail the structure of the phase space of a reversible dynamical system describing the stationary solutions of a model for a nonlinear optical cavity. We compare our results with the general picture described in [P.D. Woods, A.R. Champneys, Physica D 129 (1999) 147; P. Coullet, C. Riera, C. Tresser, Phys. Rev. Lett. 84 (2000) 3069] and find that the stable and unstable manifolds of homogeneous and patterned solutions present a much higher level of complexity than predicted, including the existence of additional localized solutions and fronts. This extra complexity arises due to homoclinic and heteroclinic intersections of the invariant manifolds of low-amplitude periodic solutions, and to the fact that these periodic solutions together with the high-amplitude ones constitute a one-parameter family generating a closed line on the symmetry plane. (c) 2006 Elsevier B.V. All rights reserved.

KW - homoclinic bifurcations

KW - localized structures

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KW - dynamical systems

KW - passive optical susyems

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