Theoretical and Mathematical Physics

, Volume 66, Issue 1, pp 31–44 | Cite as

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

  • A. V. Mikhailov
  • A. B. Shabat


Integrability Condition 
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Literature Cited

  1. 1.
    A. V. Mikhailov and A. B. Shabat, Teor. Mat. Fiz.,62, 163 (1985).Google Scholar
  2. 2.
    V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz.,61, 118 (1971).Google Scholar
  3. 3.
    V. E. Zakharov, Zh. Eksp. Teor. Fiz.,65, 219 (1973).Google Scholar
  4. 4.
    M. Lakshmanan, Phys. Lett. A,61, 53 (1977).Google Scholar
  5. 5.
    L. A. Takhtajan, Phys. Lett. A,64, 235 (1977).Google Scholar
  6. 6.
    A. E. Borovik, Pis'ma Zh. Eksp. Teor. Fiz.,28, 629 (1978).Google Scholar
  7. 7.
    E. K. Skljanin, “On complete integrability of the Landau-Lifshitz equation,” Preprint LOMI E-3 [in English], LOMI, Leningrad (1979).Google Scholar
  8. 8.
    D. J. Kaup and A. C. Newell, J. Math. Phys.,19, 898 (1978).Google Scholar
  9. 9.
    H. H. Chen, Y. C. Lee, and C. S. Liu, Phys. Scr.,20, 490 (1979).Google Scholar
  10. 10.
    M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia (1981). p. 238.Google Scholar
  11. 11.
    A. V. Mikhailov, Pis'ma Zh. Eksp. Teor. Fiz.,30, 443 (1979).Google Scholar
  12. 12.
    A. V. Mikhailov, in: Soliton Theory. Proc. Soviet-American Symposium on Soliton Theory (eds. S. V. Manakov and V. E. Zakharov), Kiev (1979); Physica (Utrecht),3D, 73 (1981).Google Scholar
  13. 13.
    V. V. Sokolov, and A. B. Shabat, Funktsional. Analiz i Ego Prilozhen.,14, 79 (1980).Google Scholar
  14. 14.
    A. G. Rieman, Zap. Nauchn. Semin. LOMI,95, 3 (1980).Google Scholar
  15. 15.
    F. W. Nijhoff, G. R. W. Quispel, J. van der Linden, and H. W. Capel, “On some linear integrable equations generating solitons of nonlinear partial differential equations,” Preprint, Lorenz voor Theoretische Naturkunde Institute, Leiden (1982).Google Scholar
  16. 16.
    M. Wadati, K. Konno, and Y. Ichikawa, J. Phys. Soc. Jpn.,47, 1698 (1979).Google Scholar
  17. 17.
    D. J. Kaup, Prog. Theor. Phys.,54, 296 (1975).Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • A. V. Mikhailov
  • A. B. Shabat

There are no affiliations available

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