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Functional Analysis and Its Applications

, Volume 17, Issue 4, pp 247–251 | Cite as

Method of the inverse scattering problem with spectral parameter on an algebraic curve

  • V. E. Zakharov
  • A. V. Mikhailov
Article

Keywords

Functional Analysis Spectral Parameter Algebraic Curve Inverse Scattering Scattering Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature Cited

  1. 1.
    V. E. Zakharov and A. B. Shabat, "Integration of nonlinear equations of mathematical physics by the method of the inverse scattering problem," Funkts. Anal.,13, No. 3, 13–21 (1979).Google Scholar
  2. 2.
    V. E. Zakharov and A. V. Mikhailov, "Relativistically invariant two-dimensional models of field theory, integrable by the method of the inverse scattering problem," Zh. Eksp. Teor. Fiz.,74, No. 6, 1953–1973 (1978).Google Scholar
  3. 3.
    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).Google Scholar
  4. 4.
    A. V. Mikhailov, "The reduction problem and the inverse scattering method," Physica,3D, Nos. 1 & 2, 73–117 (1981).Google Scholar
  5. 5.
    A. V. Mikhailov, "Reduction in integrable systems. Group of reductions," Pis'ma Zh. Eksp. Teor. Fiz.,32, No. 2, 187–192 (1980).Google Scholar
  6. 6.
    E. K. Sklyanin, "On complete integrability of the Landau—Lifschitz equation," Preprint LOMI, E-3-79, Leningrad (1979).Google Scholar
  7. 7.
    I. V. Cherednik, "Integrability of the equations of a two-dimensional asymmetric chiral O(3)-field and its quantum analog," Yad. Fiz.,33, No. 1, 278–282 (1981).Google Scholar
  8. 8.
    A. V. Mikhailov, "The Landau—Lifschitz equation and the Riemann boundary problem on a torus," Phys. Lett.,92A, No. 2, 51–55 (1982).Google Scholar
  9. 9.
    Yu. L. Rodin, "The Riemann boundary problem on a torus and the inverse scattering problem for the Landau—Lifschitz equation," Lett. Math. Phys.,7, 3–8 (1983).Google Scholar
  10. 10.
    I. M. Krichever and S. P. Novikov, "Holomorphic bundles and nonlinear equations," Physica,3D, Nos. 1 & 2, 267–293 (1981).Google Scholar
  11. 11.
    V. E. Zakharov and L. A. Takhtadzhyan, "Equivalence of the nonlinear Schrodinger equation and the Heisenberg ferromagnetics equation," Teor. Mat. Fiz.,38, No. 1, 26–35 (1979).Google Scholar
  12. 12.
    B. Saint-Donat, C. R. Acad. Sci.,274A, No. 4, 324–327 (1972).Google Scholar
  13. 13.
    Yu. A. Rodin, "Solvability conditions for Riemann—Hilbert boundary problems on Riemann surfaces," Dokl. Akad. Nauk SSSR,129, No. 6, 1234–1237 (1959).Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • V. E. Zakharov
  • A. V. Mikhailov

There are no affiliations available

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