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Expansions with respect to squares, symplectic and poisson structures associated with the Sturm-Liouville problem. I

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Literature Cited

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

    Google Scholar 

  2. P. P. Kulish and A. G. Reiman, Zap. Nauchn. Semin. LOMI,77, 134 (1978).

    Google Scholar 

  3. I. M. Gel'fand and I. Ya. Dorfman, Funktsional. Analiz i Ego Prilozhen.,14, 71 (1980);15, 23 (1981).

    Google Scholar 

  4. V. Barcilon, J. Math. Phys.,15, 429 (1974).

    Google Scholar 

  5. K. P. Kirchev and E. Kh. Khristov, SMZh.,21, 98 (1980).

    Google Scholar 

  6. A. C. Newell, “The inverse scattering transform,” in: Solitons (eds. R. K. Bullough and P. J. Caudrey), Springer, Berlin (1980).

    Google Scholar 

  7. E. Kh. Khristov, Differen. Equations,19, 1548 (1983).

    Google Scholar 

  8. M. J. Ablowitz, D. J. Kaup, A. C. Newel, and H. Segur, Stud. Appl. Math.,53, 249 (1974).

    Google Scholar 

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

    Google Scholar 

  10. I. M. Krichever, Dokl. Akad. Nauk SSSR,270, 1312 (1983).

    Google Scholar 

  11. L. D. Faddeev and L. A. Takhtajan, Lett. Math. Phys.,10, 231 (1985).

    Google Scholar 

  12. V. S. Buslaev, L. D. Faddeev, and L. A. Takhtajan, Physica (Utrecht) D,18, 255 (1986).

    Google Scholar 

  13. F. Calogero and A. Degasperis, Spectral Transform and Solitons: Tools to Solve and Investigate Nonlinear Evolution Equations, Vol. 1 (Studies in Math. and its Applications, Vol. 13), North-Holland, Amsterdam (1982).

    Google Scholar 

  14. L. A. Lyusternik and V. I. Sobolev, Elements of Functional Analysis [in Russian], Nauka, Moscow (1965).

    Google Scholar 

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V. A. Steklov Mathematics Institute, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 72, No. 3, pp. 323–339, September, 1987.

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Arkad'ev, V.A., Pogrebkov, A.K. & Polivanov, M.K. Expansions with respect to squares, symplectic and poisson structures associated with the Sturm-Liouville problem. I. Theor Math Phys 72, 909–920 (1987). https://doi.org/10.1007/BF01018296

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  • DOI: https://doi.org/10.1007/BF01018296

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