Functional Analysis and Its Applications

, Volume 8, Issue 3, pp 226–235 | Cite as

A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I

  • V. E. Zakharov
  • A. B. Shabat
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    C. S. Gardner, J. M. Green, M. Kruskal, and R. M. Miura, "Method for solving the Korteweg—de Vries equation," Phys. Rev. Lett.,19, 1095–1097 (1967).Google Scholar
  2. 2.
    P. D. Lax, "Integrals of nonlinear equations of evolution and solitary waves," Comm. Pure Appl. Math.,21, 467–490 (1968).Google Scholar
  3. 3.
    V. E. Zakharov and A. B. Shabat, "A refined theory of two-dimensional self-focussing and one-dimensional self-modulation of waves in nonlinear media," Zh. Éksp. Teor. Fiz.,61, No. 1, 118–134 (1971).Google Scholar
  4. 4.
    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
  5. 5.
    V. E. Zakharov, "The method of the inverse scattering problem," in: Theory of Elastic Media with Microstructure, edited by I. A. Kukin [in Russian], Nauka, Moscow (1974).Google Scholar
  6. 6.
    A. B. Shabat, "Concerning the Korteweg—de Vries equation," Dokl. Akad. Nauk SSSR,211, No. 6, 1310–1313 (1973).Google Scholar
  7. 7.
    V. E. Zakharov, "On the problem of one-dimensional stochastized circuits of nonlinear oscillators," Zh. Éksp. Teor. Fiz.,65, No. 1, 219–225 (1973).Google Scholar
  8. 8.
    B. B. Kadomtsev and V. I. Petviashvili, "On the stability of solitary waves in weakly dispersive media," Dokl. Akad. Nauk SSSR,192, No. 4, 753–756 (1970).Google Scholar
  9. 9.
    M. Wadati and M. Toda, "Exact N-soliton solution of the Korteweg—de Vries equation," J. Phys. Soc. Japan,36, 1403–1412 (1972).Google Scholar
  10. 10.
    V. E. Zakharov and S. V. Manakov, "On resonance interaction of wave packets in nonlinear media," ZhÉTF Pis. Red.,18, No. 7, 413 (1973).Google Scholar
  11. 11.
    N. Bloembergen, Nonlinear Optics, W. A. Benjamin (1965).Google Scholar
  12. 12.
    V. E. Zakharov, L. A. Takhtadzhyan, and L. D. Faddeev, "Complete description of the solutions of the ‘sin—gordon’ equation," Dokl. Akad. Nauk SSSR (1974).Google Scholar
  13. 13.
    S. V. Manakov, "On a theory of the two-dimensional stationary self-focussing electromagnetic waves," Zh. Éksp. Teor. Fiz.,65, 505–516 (1973).Google Scholar
  14. 14.
    M. Wadati, "The modified Korteweg—de Vries equation," J. Phys. Soc. Japan,34, No. 5, 1289–1291 (1973).Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • V. E. Zakharov
  • A. B. Shabat

There are no affiliations available

Personalised recommendations