Theoretical and Mathematical Physics

, Volume 62, Issue 2, pp 107–122 | Cite as

Integrability conditions for systems of two equations of the form u t =A(u)u xx +F(u, u x ). I

  • A. V. Mikhailov
  • A. B. Shabat
Article

Keywords

Integrability Condition 

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Literature Cited

  1. 1.
    M. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia (1981).Google Scholar
  2. 2.
    V. V. Sokolov and A. B. Shabat, Sov. Sci. Rev. C,4, 221 (1984).Google Scholar
  3. 3.
    F. B. Estabrook and H. D. Wahlquist, J. Math. Phys.,16, 1 (1975).Google Scholar
  4. 4.
    F. B. Estabrook and H. D. Wahlquist, J. Math. Phys.,17, 1293 (1976).Google Scholar
  5. 5.
    N. Kh. Ibragimov and A. B. Shabat, Funktsional. Analiz i Ego Prilozhen.,14, 79 (1980).Google Scholar
  6. 6.
    V. V. Golubev, Lectures on the Mathematical Theory of Differential Equations [in Russian], Gostekhizdat, Moscow (1950).Google Scholar
  7. 7.
    A. V. Zhiber, and A. B. Shabat, Dokl. Akad. Nauk SSSR,247 1103 (1979).Google Scholar
  8. 8.
    S. I. Svinolupov and V. V. Sokolov, Funktsional. Analiz i Ego Prilozhen.,16, 86 (1982).Google Scholar
  9. 9.
    R. I. Yamilov, Usp. Mat. Nauk,38, 155 (1983).Google Scholar
  10. 10.
    P. D. Lax, Commun. Pure Appl. Math.,21, 467 (1968).Google Scholar
  11. 11.
    F. Magri, J. Math. Phys.,19, 1156 (1978).Google Scholar
  12. 12.
    V. E. Zakharov and E. P. Schulman, Physica (Utrecht),4D, 270 (1982).Google Scholar
  13. 13.
    A. P. Fordi and P. P. Kulish, Commun. Math. Phys.,89, 427 (1983).Google Scholar
  14. 14.
    E. K. Sklvanin, “On complete integrability of the Landau-Lifshitz equation,” Preprint E-3-1979 [in English], LOMI, Leningrad (1979).Google Scholar
  15. 15.
    M. Wadati, K. Konno, and Y. H. Ichikawa, J. Phys. Soc. Jpn.,47, 1968 (1979).Google Scholar
  16. 16.
    I. M. Gel'fand and L. A. Dikii, Funktsional. Analiz i Ego Prilozhen.,10, 13 (1976).Google Scholar
  17. 17.
    Yu. I. Manin, Modern Problems of Mathematics, Vol. 11 [in Russian], VINITI, Moscow (1978), pp. 5–152.Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • A. V. Mikhailov
  • A. B. Shabat

There are no affiliations available

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