IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v38y2008i1p238-253.html
   My bibliography  Save this article

Integrable vortex dynamics in anisotropic planar spin liquid model

Author

Listed:
  • Gurkan, Zeynep Nilhan
  • Pashaev, Oktay

Abstract

The problem of magnetic vortex dynamics in an anisotropic spin liquid model is considered. For incompressible flow the model admits reduction to saturating Bogomolny inequality analytic projections of spin variables, subject the linear holomorphic Schrödinger equation. It allows us to construct N vortex configurations in terms of the complex Hermite polynomials. Using complex Galilean boost transformations, the interaction of the vortices and the vortex chain lattices (vortex crystals) is studied. By the complexified Cole–Hopf transformation, integrable N vortex dynamics is described by the holomorphic Burgers equation. Mapping of the point vortex problem to N-particle problem, the complexified Calogero–Moser system, showing its integrability and the Hamiltonian structure, is given.

Suggested Citation

  • Gurkan, Zeynep Nilhan & Pashaev, Oktay, 2008. "Integrable vortex dynamics in anisotropic planar spin liquid model," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 238-253.
  • Handle: RePEc:eee:chsofr:v:38:y:2008:i:1:p:238-253
    DOI: 10.1016/j.chaos.2006.11.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906010472
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2006.11.013?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. El Naschie, M.S., 2006. "Holographic dimensional reduction: Center manifold theorem and E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 816-822.
    2. El Naschie, M. Saladin, 2006. "Nanotechnology for the developing world," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 769-773.
    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. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
    2. El Naschie, M.S., 2007. "Determining the number of Fermions and the number of Boson separately in an extended standard model," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1241-1243.
    3. Mursaleen, M. & Mohiuddine, S.A., 2009. "On stability of a cubic functional equation in intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2997-3005.
    4. Chen, Ning & Li, Zichuan & Jin, Yuanyuan, 2009. "Visual presentation of dynamic systems with hyperbolic planar symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 621-634.
    5. He, Ji-Huan & Liu, Yong & Xu, Lan & Yu, Jian-Yong, 2007. "Micro sphere with nanoporosity by electrospinning," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1096-1100.
    6. El Naschie, M.S., 2007. "The Fibonacci code behind super strings and P-Branes. An answer to M. Kaku’s fundamental question," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 537-547.
    7. He, Ji-Huan, 2008. "String theory in a scale dependent discontinuous space–time," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 542-545.
    8. He, Ji-Huan & Wan, Yu-Qin & Xu, Lan, 2007. "Nano-effects, quantum-like properties in electrospun nanofibers," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 26-37.
    9. El Naschie, M.S., 2007. "Estimating the experimental value of the electromagnetic fine structure constant α¯0=1/137.036 using the Leech lattice in conjunction with the monster group and Spher’s kissing number in 24 dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 383-387.
    10. El-Okaby, Ayman A., 2008. "The exceptional E-infinity theory holographic boundary, F-theory and the number of particles in the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1286-1291.
    11. He, Ji-Huan & Liu, Yong & Xu, Lan & Yu, Jian-Yong & Sun, Gang, 2008. "BioMimic fabrication of electrospun nanofibers with high-throughput," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 643-651.
    12. Marek-Crnjac, L., 2007. "Fuzzy Kähler manifolds," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 677-681.
    13. Marek-Crnjac, L., 2009. "A short history of fractal-Cantorian space-time," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2697-2705.
    14. El Naschie, M.S., 2007. "SU(5) grand unification in a transfinite form," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 370-374.
    15. Elokaby, A., 2009. "On the deep connection between instantons and string states encoder in Klein’s modular space," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 303-305.
    16. Jiang, Weihua & Wang, Hongbin & Wei, Junjie, 2008. "A study of singularities for magnetic bearing systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 715-719.
    17. Mursaleen, M. & Mohiuddine, S.A., 2009. "Nonlinear operators between intuitionistic fuzzy normed spaces and Fréchet derivative," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1010-1015.
    18. Pardo-Guerra, Juan Pablo, 2011. "Mapping emergence across the Atlantic: Some (tentative) lessons on nanotechnology in Latin America," Technology in Society, Elsevier, vol. 33(1), pages 94-108.
    19. El Naschie, M.S., 2008. "Deriving the largest expected number of elementary particles in the standard model from the maximal compact subgroup H of the exceptional Lie group E7(-5)," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 956-961.
    20. El Naschie, M.S., 2007. "A derivation of the electromagnetic coupling α0≃137.036," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 521-526.

    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:38:y:2008:i:1:p:238-253. 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.