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SIGMA, 2008, Volume 4, 041, 16 pages (Mi sigma294)  

This article is cited in 7 scientific papers (total in 7 papers)

Integrable String Models in Terms of Chiral Invariants of $\mathrm{SU}(n)$, $\mathrm{SO}(n)$, $\mathrm{SP}(n)$ Groups

Victor D. Gershun

ITP, NSC Kharkiv Institute of Physics and Technology, Kharkiv, Ukraine

Abstract: We considered two types of string models: on the Riemmann space of string coordinates with null torsion and on the Riemman–Cartan space of string coordinates with constant torsion. We used the hydrodynamic approach of Dubrovin, Novikov to integrable systems and Dubrovin solutions of WDVV associativity equation to construct new integrable string equations of hydrodynamic type on the torsionless Riemmann space of chiral currents in first case. We used the invariant local chiral currents of principal chiral models for $\mathrm{SU}(n)$, $\mathrm{SO}(n)$, $\mathrm{SP}(n)$ groups to construct new integrable string equations of hydrodynamic type on the Riemmann space of the chiral primitive invariant currents and on the chiral non-primitive Casimir operators as Hamiltonians in second case. We also used Pohlmeyer tensor nonlocal currents to construct new nonlocal string equation.

Keywords: string; integrable models; Poisson brackets; Casimir operators; chiral currents

DOI: https://doi.org/10.3842/SIGMA.2008.041

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Full text: http://emis.mi.ras.ru/.../041
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Bibliographic databases:

ArXiv: 0805.0656
MSC: 81T20; 81T30; 81T40; 37J35; 53Z05; 22E70
Received: October 30, 2007; in final form April 22, 2008; Published online May 6, 2008
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Citation: Victor D. Gershun, “Integrable String Models in Terms of Chiral Invariants of $\mathrm{SU}(n)$, $\mathrm{SO}(n)$, $\mathrm{SP}(n)$ Groups”, SIGMA, 4 (2008), 041, 16 pp.

Citation in format AMSBIB
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\by Victor D.~Gershun
\paper Integrable String Models in Terms of Chiral Invariants of $\mathrm{SU}(n)$, $\mathrm{SO}(n)$,
$\mathrm{SP}(n)$ Groups
\jour SIGMA
\yr 2008
\vol 4
\papernumber 041
\totalpages 16
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\crossref{https://doi.org/10.3842/SIGMA.2008.041}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-83055186292}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Mohammedi N., “On the geometry of classically integrable two-dimensional non-linear sigma models”, Nuclear Phys. B, 839:3 (2010), 420–445  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Gershun V.D., “Integrable string models with constant torsion in terms of chiral invariants of $SU(n)$, $SO(n)$, $SP(n)$ groups”, Phys. Atomic Nuclei, 73:2 (2010), 304–310  crossref  adsnasa  isi  scopus
    3. Gershun, V.D., “Integrable string models with constant SU(3) torsion”, Physics of Particles and Nuclei Letters, 8:3 (2011), 293–298  crossref  adsnasa  scopus
    4. Gershun V.D., “Integrable WZNW Models and String Models of WZNW Model Type With Constant $SU(2)$ Torsion”, Problems of Atomic Science and Technology, 2012, no. 1, 337–341  isi
    5. Gershun V.D., “Integrable String Models of WZNW Model Type with Constant Su(2), So(3), Sp(2) and Su(3) Torsion and Hydrodynamic Chains”, Phys. Part. Nuclei, 43:5 (2012), 659–662  crossref  adsnasa  isi  elib  scopus
    6. Cirilo-Lombardo D.J., “Integrable Hydrodynamic Equations For Initial Chiral Currents and Infinite Hydrodynamic Chains From WZNW Model and String Model of WZNW Type With Su(2), So(3), Sp(2), Su(Infinity), So(Infinity), Sp(Infinity) Constant Torsions”, Int. J. Mod. Phys. A, 29:24 (2014), 1450134  crossref  zmath  adsnasa  isi  elib  scopus
    7. Mohammedi N., “Classically Integrable Two-Dimensional Non-Linear SIGMA Models”, Proceedings of the Sixteenth International Conference on Geometry, Integrability and Quantization, eds. Mladenov I., Ludu A., Yoshioka A., Inst Biophysics & Biomedical Engineering Bulgarian Acad Sciences, 2015, 250–255  crossref  mathscinet  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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