Bifurcation structure of dissipative solitons

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Gomila, Damia and Scroggie, A. J. and Firth, W. J. (2007) Bifurcation structure of dissipative solitons. Physica D: Nonlinear Phenomena, 227 (1). pp. 70-77. ISSN 0167-2789 (https://doi.org/10.1016/j.physd.2006.12.008)

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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.

  • Item type:Article
    ID code:31022
    Dates:
    Date
    Event
    1 March 2007
    Published
    Subjects:Science > Physics > Optics. Light
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:20 Jun 2011 15:46
    Last modified:11 Nov 2024 09:44
    URI:https://strathprints.strath.ac.uk/id/eprint/31022
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