Advertisement

Letters in Mathematical Physics

, Volume 105, Issue 1, pp 27–43 | Cite as

Characteristics of Conservation Laws of Chiral-Type Systems

  • A. V. Balandin
Article

Abstract

In this note, a new way to construct characteristics of conservation laws of integrable chiral-type systems is proposed. Some examples of such characteristics are considered.

Keywords

chiral-type systems Lax representation characteristics of conservation laws Killing fields 

Mathematics Subject Classification

35Q51 37K10 37K05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Balandin A.V., Pakhareva O.N., Potemin G.V.: Lax representation of the chiral-type field equations. Phys. Lett. A. 23, 168–176 (2001)ADSCrossRefGoogle Scholar
  2. 2.
    Demskoi D.K., Meshkov A.G.: Zero-curvature representation for a chiral-type three-field system. Inverse Probl. 19, 563–571 (2003)ADSCrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    Goto, M., Grosshans, F.D.: Semisimple lie algebras. Lecture notes in pure and applied mathematics. 38 (1978)Google Scholar
  4. 4.
    Gu, C., Hu, H., Zhou, Z.: Darboux transformations in integrable systems. Theory and their applications to geometry, Springer (2005)Google Scholar
  5. 5.
    Kostant B.: Lie group representations on polynomial rings. Am. J. Math. 85, 327–404 (1963)CrossRefMathSciNetMATHGoogle Scholar
  6. 6.
    Leznov, A.N., Savel’ev, M.V.: Group-theoretical methods for integration of nonlinear dynamical systems, Birkhauser (1992)Google Scholar
  7. 7.
    Lund F., Regge T.: Unified approach to strings and vortices with soliton solutions. Phys. Rev. D. 14, 1524–1535 (1976)ADSCrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    Marvan, M.: On zero-curvature representations of partial differential equations. In: Kowalski, O., Krupka, D. (eds.) 5th International Conference on Differential Geometry and Its Applications. pp. 103–122, Opava, Czech Republic, http://www.emis.de/proceedings/5ICDGA (1993)
  9. 9.
    Novokshenov, V.Y.: Vvedenie v teoriju solitonov. IKI, Izhevsk (in Russian) (2002)Google Scholar
  10. 10.
    Olver, P.: Applications of Lie Groups to Differential Equations, 2nd edn. Springer, New York (1993)Google Scholar
  11. 11.
    Shabat, A.B. (ed.): Encyclopedia of integrable systems. version 0043, L.D. Landau Institute for Theoretical Physics, Moscow (2010)Google Scholar
  12. 12.
    Varadarajan V.S.: On the ring of invariant polynomials on a semisimple Lie algebra. Am. J. Math. 90, 308–317 (1968)CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Mathematics and MechanicsN.I.Lobatchevsky Nizhny Novgorod State UniversityNizhny NovgorodRussia

Personalised recommendations