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Algebras of virasoro type, riemann surfaces and structures of the theory of solitons

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Literature Cited

  1. S. Mandelstam, "Dual resonance models," Phys. Rep.,13, 259–353 (1974).

    Google Scholar 

  2. A. Belavin, A. Zamolodchkov, and A. Polyakov, "An infinite conformal group in quantum field theory," Preprint, Inst. Theor. Phys., Moscow (1983).

    Google Scholar 

  3. D. Friedan, in: Recent Advances in Field Theory and Statistical Mechanics, North-Holland, Les Houches (1984).

    Google Scholar 

  4. A. A. Belavin and V. Knizhnik, "Complex geometry and the theory of quantum strings," Zh. Éksp. Teor. Fiz.,91, No. 2(8), 364–391 (1986).

    Google Scholar 

  5. J. N. Shwartz, "Superstring theory," Phys. Reports,89, 223–322 (1982).

    Google Scholar 

  6. B. L. Feigin and D. B. Fuks, "Skew-symmetric invariant differential operators on the line and Verma modules over the Virasoro algebra," Funkts. Anal. Prilozhen.,16, No. 2, 47–63 (1982).

    Google Scholar 

  7. D. Mumford, "On the stability of the algebraic variaters," Math. E'ns L'Ens,23, 39–55 (1977).

    Google Scholar 

  8. I. M. Krichever, "Algebraic curves and nonlinear difference equations," Usp. Mat. Nauk,33, No. 4, 215–216 (1978).

    Google Scholar 

  9. I. M. Krichever, "Spectral theory of ‘finite-zone’ nonstationary Schrödinger operators. Nonstationary Peierls model," Funkts. Anal. Prilozhen.,20, No. 2, 42–54 (1986).

    Google Scholar 

  10. I. V. Cherednik, "Differential equations for Baker—Akhiezer functions," Funkts. Anal. Prilozhen.,12, No. 3, 45–54 (1978).

    Google Scholar 

  11. B. A. Dubrovin, V. B. Matveev, and S. P. Novikov, "Nonlinear equations of Korteweg—de Vries type, finite-zone linear operators and Abelian varieties," Usp. Mat. Nauk,31, No. 1, 55–136 (1976).

    Google Scholar 

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

    Google Scholar 

  13. I. M. Krichever, "Methods of algebraic geometry in the theory of nonlinear equations," Usp. Mat. Nauk,32, No. 6, 183–208 (1977).

    Google Scholar 

  14. B. A. Dubrovin, "Theta-functions and nonlinear equations," Usp. Mat. Nauk,36, No. 2, 11–80 (1981).

    Google Scholar 

  15. I. M. Krichever and S. P. Novikov, "Holomorphic bundles over algebraic curves and nonlinear equations," Usp. Mat. Nauk,35, No. 6, 47–68 (1980).

    Google Scholar 

  16. B. A. Dubrovin, I. M. Krichever, and S. P. Novikov, "Integrable systems. I," in: Contemporary Problems of Mathematics: Fundamental Directions [in Russian], Itogi Nauki i Tekhniki, VINITI AN SSSR, Moscow, Vol. 4 (1985), pp. 210–315.

    Google Scholar 

  17. I. M. Krichever, "Laplace's method, algebraic curves, and nonlinear equations," Funkts. Anal. Prilozhen.,18, No. 3, 43–56 (1984).

    Google Scholar 

  18. H. Bateman and A. Erdelyi, Higher Transcendental Functions [Russian translation], Nauka, Moscow (1974).

    Google Scholar 

  19. B. A. Dubrovin, I. M. Krichever, and S. P. Novikov, "Schrödinger's equation in a periodic field and Riemann surfaces," Dokl. Akad. Nauk SSSR,229, No. 1, 15–18 (1976).

    Google Scholar 

  20. I. M. Krichever, "Algebrogeometric construction of Zakharov—Shabat equations and their periodic solutions," Dokl. Akad. Nauk SSSR,227, No. 2, 291–294 (1976).

    Google Scholar 

  21. A. Yu. Orlov and E. I. Shul'man, "Supplementary symmetries of integrable systems and representations of conformal algebra," Inst. Avtomatiki i Élektrometrii Sib. Otd. Akad. Nauk SSSR, Novosibirsk, Preprint No. 217 (1984).

    Google Scholar 

  22. A. Yu. Orlov and E. I. Shul'man, "Supplementary symmetries of two-dimensional integrable systems," Inst. Avtom. i Élektrometrii Sib. Otd. AN SSSR, Novosibirsk, Preprint No. 277 (1985).

    Google Scholar 

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G. M. Krzhizhanovskii Energy Institute. L. D. Landau Institute of Theoretical Physics. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 21, No. 2, pp. 46–63, April–June, 1987.

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Krichever, I.M., Novikov, S.P. Algebras of virasoro type, riemann surfaces and structures of the theory of solitons. Funct Anal Its Appl 21, 126–142 (1987). https://doi.org/10.1007/BF01078026

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  • DOI: https://doi.org/10.1007/BF01078026

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