Functional Analysis and Its Applications

, Volume 8, Issue 3, pp 236–246 | Cite as

The periodic problem for the Korteweg—de vries equation

  • S. P. Novikov


Functional Analysis Periodic 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    N. I. Akhiezer, "A continuum analog of orthogonal polynomials in a system of integrals," Dokl. Akad. Nauk SSSR,141, No. 2, 263–266 (1961).Google Scholar
  2. 2.
    I. M. Gel'fand and B. M. Levitan, "On the determination of a differential operator from its spectral function," Izv. Akad. Nauk SSSR, Ser. Matem.,15, 309–360 (1951).Google Scholar
  3. 3.
    V. A. Marchenko, "Some questions in the theory of one-dimensional differential operators, I," Trudy Mosk. Matem. Obshch. I, 327–420 (1952).Google Scholar
  4. 4.
    L. D. Faddeev, "Properties of the S-matrix of the one-dimensional Schrödinger equation," Trudy Matem. Inst. im. V. A. Steklova,73, 314–336 (1964).Google Scholar
  5. 5.
    C. Gardner, J. Green, M. Kruskal, and R. Miura, "A method for solving the Kortweg—de Vries equation," Phys. Rev. Lett.,19, 1095–1098 (1967).Google Scholar
  6. 6.
    R. M. Miura, C. S. Gardner, and M. Kruskal, "Kortweg—de Vries equation and generalizations," J. Math. Phys.,9, No. 8, 1202–1209 (1968).Google Scholar
  7. 7.
    P. Lax, "Integrals of nonlinear equations of evolution and solitary waves," Comm. Pure Appl. Math.,21, No. 2, 467–490 (1968).Google Scholar
  8. 8.
    V. E. Zakharov and L. D. Faddeev, "The Kortweg—de Vries equation — a completely integrable Hamiltonian system," Funkt. Analiz.,5, No. 4, 18–27 (1971).Google Scholar
  9. 9.
    V. E. Zakharov, "A kinetic equation for solitons," Zh. Éksp. Teor. Fiz.,60, No. 3, 993–1000 (1971).Google Scholar
  10. 10.
    V. E. Zakharov and A. B. Shabat, "An exact theory of two-dimensional self-focusing and one-dimensional automodulation of waves in nonlinear media," Zh. Éksp. Teor. Fiz.,61, No. 1, 118–134 (1971).Google Scholar
  11. 11.
    A. B. Shabat, "On Kortweg—de Vries equations," Dokl. Akad. Nauk SSSR,211, No. 6, 1310–1313 (1973).Google Scholar
  12. 12.
    V. E. Zakharov and A. B. Shabat, "On the interaction of solitons in a stable medium," Zh. Éksp. Teor. Fiz.,64, No. 5, 1627–1639 (1973).Google Scholar
  13. 13.
    R. Hirota, "Exact solution of the modified Korteweg—de Vries equation for multiple collisions of solitons," J. Phys. Soc. Japan,33, No. 5, 1456–1458 (1972).Google Scholar
  14. 14.
    E. L. Ince, "Further investigations into the periodic Lamé functions," Proc. Roy. Soc. Edinburgh,60, 83–99 (1940).Google Scholar
  15. 15.
    B. B. Kadomtsev and V. I. Karpman, "Nonlinear waves," Usp. Fiz. Nauk,103, No. 2, 193–232 (1971).Google Scholar
  16. 16.
    V. E. Zakharov and S. B. Manakov, "On the complete integrability of the nonlinear Schrödinger equation," Zh. Matem. i Teor. Fiz.,19, No. 3, 322–343 (1974).Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • S. P. Novikov

There are no affiliations available

Personalised recommendations