Skip to main content
SpringerLink
Log in

A generalization of the Kac-Moody algebras with a parameter on an algebraic curve and perturbations of solitons

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

The Lie-algebraic approach for the dynamic systems associated with a generalization of the Kac-Moody algebras on Riemann surfaces is developed. A technique of solving the inverse scattering problem of operators with spectral parameters on Riemann surfaces is presented. Some equations associated with generalized Kac-Moody algebras are presented. The connection between their hamiltonian structure and deformed Lax representation is discussed as well as its applications to some special perturbations of integrable systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kostant, B.: The solution to a generalization Toda lattice and representation theory. Adv. Math.34, 195–338 (1979)

    Article  Google Scholar 

  2. Takhtajan, L.A., Faddeev, L.D.: Hamiltonian approach in soliton theory. Berlin, Heidelberg, New York: Springer 1985

    Google Scholar 

  3. Mikhalev, V.G.: Complete integrability of the asymmetric chiralO(3)-field equation in a class of rapidly decreasing functions. Physica D40, 421–432 (1989)

    Google Scholar 

  4. Krichever, I.M., Novikov, S.P.: The algebras of Virasoro type, Riemann surfaces and structures of soliton theory. Funkz. Analiz.21, 46–63 (1987)

    Google Scholar 

  5. Semenov-Tyan-Shansky, M.A.: What is a classicalr-matrix? Funkz. Analiz.17, 17–33 (1983)

    Google Scholar 

  6. Zakharov, V.E., Mikhaylov, A.V.: Funkz. Analiz.17, 1–10 (1983)

    Google Scholar 

  7. Zakharov, V.E., Manakov, S.V., Novikov, S.P., Pitaevski, L.P.: Theory of solitons. Moscow: Nauka 1980

    Google Scholar 

  8. Karpman, V., Maslov, E.: The soliton perturbation theory. Sov. J. Phys. (ZETP)73, 538–559 (1977)

    Google Scholar 

  9. Kaup, D., Newell, A.: Solitons as particles and oscillators. Proc. R. Soc. London361A, 413–446 (1978)

    Google Scholar 

  10. McLaughlin, D., Scott, A.: Appl. Phys. Lett.30, 545 (1978)

    Article  Google Scholar 

  11. Mikhalev, V.G.: The investigation of the nonlinear one-dimensional systems by hamiltonian formalism. Teor. Mat. Fiz.76, 199–206 (1988)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Sciences, Vladimir State Teachers Institute, Prospect Stroiteley II, SU-600024, Vladimir, USSR

    V. G. Mikhalev

Authors
  1. V. G. Mikhalev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Ya. G. Sinai

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mikhalev, V.G. A generalization of the Kac-Moody algebras with a parameter on an algebraic curve and perturbations of solitons. Commun.Math. Phys. 134, 633–646 (1990). https://doi.org/10.1007/BF02098450

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02098450

Keywords

Search

Navigation