IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v40y2009i1p91-105.html
   My bibliography  Save this article

Spatiotemporal structure of pulsating solitons in the cubic–quintic Ginzburg–Landau equation: A novel variational formulation

Author

Listed:
  • Mancas, Stefan C.
  • Roy Choudhury, S.

Abstract

Comprehensive numerical simulations (reviewed in Dissipative Solitons, Akhmediev and Ankiewicz (Eds.), Springer, Berlin, 2005) of pulse solutions of the cubic–quintic Ginzburg–Landau Equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. The numerical simulations also reveal very interesting bifurcations sequences of these pulses as the parameters of the CGLE are varied.

Suggested Citation

  • Mancas, Stefan C. & Roy Choudhury, S., 2009. "Spatiotemporal structure of pulsating solitons in the cubic–quintic Ginzburg–Landau equation: A novel variational formulation," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 91-105.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:1:p:91-105
    DOI: 10.1016/j.chaos.2007.07.046
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907005371
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.07.046?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mancas, Stefan & Choudhury, S. Roy, 2006. "Bifurcations and competing coherent structures in the cubic-quintic Ginzburg–Landau equation I: Plane wave (CW) solutions," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1256-1271.
    2. Zhang, Jin-Liang & Wang, Ming-Liang & Gao, Ke-Quan, 2007. "Exact solutions of generalized Zakharov and Ginzburg–Landau equations," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1877-1886.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Porsezian, K. & Murali, R. & Malomed, Boris A. & Ganapathy, R., 2009. "Modulational instability in linearly coupled complex cubic–quintic Ginzburg–Landau equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1907-1913.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:40:y:2009:i:1:p:91-105. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.