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Functional Analysis and Its Applications

, Volume 19, Issue 2, pp 89–101 | Cite as

Construction of higher-dimensional nonlinear integrable systems and of their solutions

  • V. E. Zakharov
  • S. V. Manakov
Article

Keywords

Functional Analysis Integrable System Nonlinear Integrable System 
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, "A scheme for the integration of nonlinear evolution equations of mathematical physics by the inverse scattering method. I," Funkts. Anal. Prilozhen.,6, No. 3, 43–53 (1974).Google Scholar
  2. 2.
    V. E. Zahkarov and A. B. Shabat, "Integration of nonlinear equations of mathematical physics by the inverse scattering method. II," Funkts. Anal. Prilozhen.,13, No. 3, 13–22 (1970).Google Scholar
  3. 3.
    S. V. Manakov, "The inverse scattering transform for time-dependent Schrödinger equation and Kadomtsev—Petviashvili equation," Physica 3D,3, Nos. 1–2, 420–427 (1981).Google Scholar
  4. 4.
    S. V. Manakov, P. Santini, and L. A. Takhtajan, "Long-time behavior of the solutions of the Kadomtsev—Petviashvili equation," Phys. Lett.,74A, 451–454 (1980).Google Scholar
  5. 5.
    D. J. Kaup, "The inverse scattering solution for the full three-dimensional three-wave resonant interaction," Studies Appl. Math.,62, 75–83 (1980).Google Scholar
  6. 6.
    M. J. Ablowitz, D. Bar Yaacov, and A. S. Fokas, "On the inverse scattering transform for the Kadomtsev—Petviashvili equation," Studies Appl. Math.,69, 135–143 (1983).Google Scholar
  7. 7.
    M. J. Ablowitz and A. S. Fokas, "On the inverse scattering for the time-dependent Schrödinger equation and the associated Kadomtsev—Petviashvili (I) equation," Studies Appl. Math.,69, 211–228 (1983).Google Scholar
  8. 8.
    V. E. Zakharov, "The inverse scattering method," in: Solitons, R. K. Bullough and P. J. Caudrey (eds.), Springer-Verlag, Berlin (1980), pp. 243–286.Google Scholar
  9. 9.
    V. E. Zakharov, "Integrable systems in multidimensional space," in: Math. Problems in Theor. Physics, Lecture Notes in Phys., Vol. 153, Springer-Verlag, Berlin (1982), pp. 190–216.Google Scholar
  10. 10.
    V. E. Zakharov, "Multidimensional integrable systems," Report to the International Congress of Math., Warsaw (1983).Google Scholar
  11. 11.
    S. V. Manakov, "Nonlocal Riemann problem and solvable multidimensional nonlinear equations," talk delivered at the NORDITA-Landau Institute Workshop, Copenhagen, September (1982).Google Scholar
  12. 12.
    V. E. Zakharov and S. V. Manankov, "Multidimensional nonlinear integrable systems and methods for constructing their solutions," Zap. Nauchn. Sem. LOMI,133, 77–91 (1984).Google Scholar
  13. 13.
    V. E. Zakharov and A. V. Mikhailov, "On the integrability of classical spinor models in two-dimensional space—time," Commun. Math. Phys.,74, 4–40 (1980).Google Scholar
  14. 14.
    V. E. Zakharov and A. V. Mikhailov, "Variational principle for the equations integrable by the method of the inverse problem," Funkts. Anal. Prilozhen.,14, No. 1, 55–56 (1980).Google Scholar
  15. 15.
    S. V. Manakov, "The inverse scattering method and two-dimensional evolution equations," Usp. Mat. Nauk,31, No. 5, 245 (1976).Google Scholar
  16. 16.
    S. K. Zhdanov and B. L. Trubnikov, "Soliton chains in a plasma with magnetic viscosity," Pis'ma Zh. Eksp. Teor. Fiz.,39, No. 3, 110–113 (1983).Google Scholar
  17. 17.
    V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevski, Theory of Solitons [in Russian], Nauka, Moscow (1980).Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • V. E. Zakharov
  • S. V. Manakov

There are no affiliations available

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