Functional Analysis and Its Applications

, Volume 13, Issue 1, pp 6–15 | Cite as

Integrable nonlinear equations and the Liouville theorem

  • I. M. Gel'fand
  • L. A. Dikii


Functional Analysis Nonlinear Equation Integrable Nonlinear Equation Liouville Theorem 
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Literature Cited

  1. 1.
    S. P. Novikov, "Periodic problem for the Korteweg—de Vries equation," Funkts. Anal. Prilozhen.,8, No. 3, 54–66 (1974).Google Scholar
  2. 2.
    B. A. Dubrovin, "The periodic Korteweg—de Vries problem in a class of finite zone potentials," Funkts. Anal. Prilozhen.,9, No. 3, 41–52 (1975).Google Scholar
  3. 3.
    A. R. Its and V. B. Matveev, "Schrödinger operators with finite-zone spectrum and Nsoliton solutions of the Korteweg—de Vries equations," Teor. Mat. Fiz.,23, No. 1, 51–68 (1975).Google Scholar
  4. 4.
    N. F. McKean and F. V. Moerbeke, "Sur le spèctre de quelques opérateurs et la variété de Jacobi," Sém. Bourbaki (1975–1976), p. 474.Google Scholar
  5. 5.
    I. M. Gel'fand and L. A. Dikii, "Asymptotics of the resolvent of Sturm—Liouville equations and the algebra of the Korteweg—de Vries equations," Usp. Mat. Nauk,20, No. 5, 67–100 (1975).Google Scholar
  6. 6.
    P. Lax, "Periodic solutions of the KdV equations," Lect. Appl. Math.,15, 85–96 (1974).Google Scholar
  7. 7.
    B. V. Yusin, "Proof of a variational relation among the coefficients of the asymptotics of a Sturm—Liouville equation," Usp. Mat. Nauk,33, No. 1, 233–234 (1978).Google Scholar
  8. 8.
    S. I. Al'ber, "Study of equations of the Korteweg—de Vries type by the method of recursion relations," Preprint (1976), pp. 1–13.Google Scholar
  9. 9.
    I. M. Gel'fand and L. A. Dikii, "Lie algebra structure in the formal calculus of variations," Funkts. Anal. Prilozhen.,10, No. 1, 18–25 (1976).Google Scholar
  10. 10.
    N. G. Chebotarev, The Theory of Algebraic Functions [in Russian], Gostekhizdat, Moscow (1948).Google Scholar

Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • I. M. Gel'fand
  • L. A. Dikii

There are no affiliations available

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