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A generalization of Darboux theorem to Hamiltonian field theory

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Literature cited

  1. C. S. Gardner, “Korteweg-de Vries equation and generalizations, IV,” J. Math. Phys.,12, No. 8, 1548–1551 (1971).

    Google Scholar 

  2. A. M. Vinogradov, “Hamiltonian structures in field theory,” Dokl. Akad. Nauk SSSR,241, No. 1, 18–21 (1978).

    Google Scholar 

  3. A. S. Fokas and B. Fuchssteiner, “On the structure of simplectic operators and hereditary symmetries,” Lett. Nuovo Cimento,28, No. 8, 299–303 (1980).

    Google Scholar 

  4. B. A. Kupershmidt and G. Wilson, “Modifying Lax equations and the second Hamiltonian structure,” Invent. Math.,62, No. 3, 403–436 (1981).

    Google Scholar 

  5. I. M. Gel'fand and I. Ya. Dorftnan, “Hamiltonian operators and the related algebraic structures,” Funkt s. Anal. Prilozhen.,13, No. 4, 13–30 (1979).

    Google Scholar 

  6. I. M. Gel'fand and I. Ya. Dorfman, “Hamiltonian operators and infinite-dimensional Lie algebras,” Funkts. Anal. Prilozhen.,14, No. 3, 23–40 (1981).

    Google Scholar 

  7. I. M. Gel'fand and I. Ya. Dorfman, “Skhouten bracket and Hamiltonian operators,” Funkts. Anal. Prilozhen.,14, No. 3, 71–74 (1980).

    Google Scholar 

  8. A. M. Vinogradov, “Geometry of nonlinear differential equations,” in: collection: Problems of Geometry [in Russian], VINITI, 11., 89–134 (1980).

  9. A. M. Vinogradov and B. A. Kupershmidt, “Structure of Hamiltonian mechanics,” Usp. Mat. Nauk,32, No, 4, 175–236 (1977).

    Google Scholar 

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Translated from Matematicheskie Zametki, Vol. 36, No. 4, pp. 537–547, October, 1984.

The author sincerely thanks A. M. Vinogradov for suggesting the problem and valuable comments.

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Astashov, A.M. A generalization of Darboux theorem to Hamiltonian field theory. Mathematical Notes of the Academy of Sciences of the USSR 36, 766–771 (1984). https://doi.org/10.1007/BF01156466

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