Skip to main content
SpringerLink
Log in

Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We consider the problem of describing the possible spectra of an acoustic operator with a periodic finite-gap density. On the moduli space of algebraic Riemann surfaces, we construct flows that preserve the periods of the corresponding operator. By a suitable extension of the phase space, these equations can be written with quadratic irrationalities.

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. E. I. Dinaburg and Ya. G. Sinai, Funct. Anal. Appl., 9, 279–289 (1975).

    Article  MATH  MathSciNet  Google Scholar 

  2. V. A. Marcenko and I. V. Ostrovskii, Sb. Math., 97, 493–554 (1975).

    MathSciNet  Google Scholar 

  3. P. G. Grinevich and M. U. Schmidt, Phys. D, 87, 73–98 (1995).

    Article  MathSciNet  Google Scholar 

  4. N. M. Ercolani, M. G. Forest, D. W. McLaughlin, and A. Sinha, J. Nonlinear Sci., 3, 393–426 (1993).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. I. M. Krichever, Comm. Pure Appl. Math., 47, 437–475 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  6. L. A. Dmitrieva, J. Phys. A, 26, 6005–6020 (1993).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. L. A. Dmitrieva, Phys. Lett. A, 182, 65–70 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  8. L. A. Dmitrieva and D. A. Pyatkin, Phys. Lett. A, 303, 37–44 (2002).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. C. Rogers and M. C. Nucci, Phys. Scripta, 33, 289–292 (1986).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. S. Tanveer, Philos. T. Roy. Soc. London Ser. A, 343, 155–204 (1993).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. H. Knörrer, J. Reine Angew. Math., 334, 69–78 (1982).

    MATH  MathSciNet  Google Scholar 

  12. J. Moser, “Various aspects of integrable Hamiltonian systems,” in: Dynamical Systems (Progr. Math., Vol. 8, J. Guckenheimer, J. Moser, and S. E. Newhouse, eds.), Birkhäuser, Boston (1980), p. 233–289.

    Google Scholar 

  13. A. P. Veselov, Funct. Anal. Appl., 14, 37–39 (1980).

    MATH  MathSciNet  Google Scholar 

  14. A. P. Veselov, Funct. Anal. Appl., 26, 211–213 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  15. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: Method of the Inverse Problem [in Russian], Nauka, Moscow (1980); English transl.: S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakharov, Theory of Solitons: The Inverse Scattering Method, Plenum, New York (1984).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Columbia University, New York, USA

    D. V. Zakharov

Authors
  1. D. V. Zakharov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. V. Zakharov.

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 1, pp. 46–57, October, 2007.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zakharov, D.V. Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation. Theor Math Phys 153, 1388–1397 (2007). https://doi.org/10.1007/s11232-007-0122-0

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-007-0122-0

Keywords

Search

Navigation