Skip to main content
SpringerLink
Log in

Korteweg-de Vries equation: A completely integrable Hamiltonian system

  • Published:
Functional Analysis and Its Applications Aims and scope

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.

Literature Cited

  1. C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, "Method for solving the Korteweg-de Vries equation," Phys. Rev. Lett.,19, 1095–1097 (1967).

    Google Scholar 

  2. R. M. Miura, C. S. Gardner, and M. D. Kruskal, "Korteweg-de Vries equation and generalizations, II. Existence of conservation laws and constants of motion," J. Math. Phys.,9, No. 8, 1204–1209 (1968).

    Google Scholar 

  3. M. D. Kruskal, R. M. Miura, C. S. Gardner, and N. J. Zabusky, "Korteweg-de Vries equation and generalizations, V. Uniqueness and nonexistence of polynomial conservation laws," J. Math. Phys.,11, No. 3, 952–960 (1970).

    Google Scholar 

  4. P. D. Lax, "Integrals of nonlinear equations and solitary waves" Comm. Pure Appl. Math.,21, No. 2, 467–490 (1968).

    Google Scholar 

  5. L. D. Faddeev, "Properties of the S-matrix of the one-dimensional Schroedinger equation," Trudy Matem. in-ta im. V. A. Steklova,73, 314–336 (1964).

    Google Scholar 

  6. J. Kay and H. E. Moses, "The determination of the scattering potential from the spectral measure function, III" Nuovo Cimento,3, No. 2, 277–304 (1956).

    Google Scholar 

  7. L. D. Landau and E. M. Lifshits, Mechanics, Addison-Wesley, Reading, Mass (1960).

    Google Scholar 

  8. V. I. Arnol'd, Lectures on Classical Mechanics [in Russian], Moscow State Univ., Moscow (1968).

    Google Scholar 

  9. I. M. Gel'fand and B. M. Levitan, "On a simple identity for the characteristic values of a differential operator of the second order," Dokl. Akad. Nauk SSSR,88, No. 4, 593–596 (1953).

    Google Scholar 

  10. I. M. Gel'fand, "On identities for characteristic values of a differentiable operator of the second order," Usp. Mat. Nauk,11, No. 1, 191–198 (1956).

    Google Scholar 

  11. V. S. Buslaev and L. D. Faddeev, "On formulas for traces of a Sturm-Liouville singular differential operator," Dokl. Akad. Nauk SSSR, 132, No. 1, 13–16 (1960).

    Google Scholar 

  12. V. E. Zakharov, "A kinetic equation for solitons," Zh. Éksp. Teor. Fiz.,60, No. 3, 993–1000 (1971).

    Google Scholar 

Download references

Authors
  1. V. E. Zakharov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. D. Faddeev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Institute of Nuclear Physics, Siberian Branch, Academy of Sciences of the USSR. Leningrad Branch, V. A. Steklov Mathematics Institute. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 5, No. 4, pp. 18–27, October–December, 1971.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zakharov, V.E., Faddeev, L.D. Korteweg-de Vries equation: A completely integrable Hamiltonian system. Funct Anal Its Appl 5, 280–287 (1971). https://doi.org/10.1007/BF01086739

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01086739

Keywords

Search

Navigation