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Hamiltonian structures for integrable models of field theory

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Literature Cited

  1. C. S. Gardner, J. M. Green, M. D. Kruskal, and R. M. Miura, Phys. Rev. Lett.,19, 1095 (1967).

    Google Scholar 

  2. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  3. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia (1981).

    Google Scholar 

  4. V. E. Zakharov and L. D. Faddeev, Funktsional. Analiz i Ego Prilozhen.,5, 18 (1971).

    Google Scholar 

  5. E. K. Sklyanin, Zap. Nauchn. Semin. LOMI,95, 55 (1980).

    Google Scholar 

  6. L. D. Faddeev, “Integrable models in 1+1 dimensional quantum field theory,” Preprint CEN-SACLAY S. Ph. T. (1982).

  7. S. Lie, Theorie der Transformationsgruppen, Vol. 3, Leipzig (1983).

  8. A. A. Kirillov, Elements of the Theory of Representations [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  9. L. A. Takhtadzhyan and L. D. Faddeev, Zap. Nauchn. Semin. LOMI,115, 264 (1982).

    Google Scholar 

  10. A. G. Reiman, Zap. Nauchn. Semin. LOMI,95, 3 (1980).

    Google Scholar 

  11. A. G. Reiman and M. A. Semenov-Tyan-Shanskii, Dokl. Akad. Nauk SSSR,261, 1310 (1980).

    Google Scholar 

  12. L. A. Takhtajan, Phys. Lett. A,64, 235 (1977).

    Google Scholar 

  13. V. E. Zakharov and S. V. Manakov, Teor. Mat. Fiz.,19, 332 (1974).

    Google Scholar 

  14. S. V. Manakov, Zh. Eksp. Teor. Fiz.,65, 505 (1973).

    Google Scholar 

  15. P. P. Kulish and A. F. Fordy, “Nonlinear Schrödinger equations and simple Lie algebras,” Preprint VMIST, Manchester (1982).

  16. É. B. Vinberg, Izv. Akad. Nauk SSSR, Ser. Mat.,40, 488 (1976).

    Google Scholar 

  17. A. A. Belavin and V. G. Drinfel'd, “Triangle equations and simple Lie algebras,” Preprint 1982-18 [in Russian], L. D. Landau Institute of Theoretical Physics, Chernogolovka (1982).

    Google Scholar 

  18. A. V. Mikhailov Physica (Utrecht),3D, 73 (1981).

    Google Scholar 

  19. E. I. Sklyanin, “On complete integrability of the Landau-Lifshitz equation,” Preprint E-3-79 [in English], Leningrad Branch, V. A. Steklov Mathematics Institute Leningrad (1979).

    Google Scholar 

  20. L. A. Takhtadzhyan and L. D. Faddeev, Teor. Mat. Fiz.,21, 160 (1974); L. D. Faddeev and V. E. Korepin, Phys. Rep.,42C, 1 (1978).

    Google Scholar 

  21. A. G. Izergin and V. E. Korepin, Dokl. Akad. Nauk SSSR,259, 76 (1981).

    Google Scholar 

  22. A. G. Izergin and V. E. Korepin, Fiz. elem. Chastits At. Yadra,13, 501 (1982).

    Google Scholar 

  23. A. G. Izergin and V. E. Korepin, Lett. Math. Phys.,5, 199 (1981).

    Google Scholar 

  24. V. G. Drinfel'd, Dokl. Akad. Nauk SSSR268, 285 (1983).

    Google Scholar 

  25. P. P. Kulish and E. K. Sklyanin, Phys. Lett. A,84, 349 (1981).

    Google Scholar 

  26. P. P. Kulish, N. Yu. Reshetikhin, and E. K. Sklyanin, Lett. Math. Phys.,5, 393 (1981).

    Google Scholar 

  27. E. K. Sklyanin, Funktsional. Analiz i Ego Prilozhen.,16, 27 (1982).

    Google Scholar 

  28. M. A. Semenov-Tyan-Shanskii, Zap. Nauchn. Semin. LOMI,123, 77 (1983).

    Google Scholar 

  29. A. G. Reyman and M. A. Semenov-Tian-Shansky, Inv. Math.,54, 81 (1979).

    Google Scholar 

  30. B. Kostant “Quantization and representation theory, Lect. Notes of London Math. Soc.,34 (1979).

  31. V. I. Smirnov, Course of Higher Mathematics, Vol. 3 [in Russian], Nauka, Moscow (1974).

    Google Scholar 

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Leningrad Branch, V. A. Steklov Mathematics Institute, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 56, No. 3, pp. 323–343, September, 1983.

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Reshetikhin, N.Y., Faddeev, L.D. Hamiltonian structures for integrable models of field theory. Theor Math Phys 56, 847–862 (1983). https://doi.org/10.1007/BF01086251

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