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Recursion operators and Hamiltonian structures in Sato's theory

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Abstract

Following Sato's famous construction of the KP hierarchy as a hierarchy of commuting Lax equations on the algebra of microdifferential operators, it is shown that n-reduction leads to a recursive scheme for these equations. Explicit expressions for the recursion operators and the Hamiltonian operators are obtained.

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References

  1. HirotaR., in R. K.Bullough and P.Caudrey (eds.), Solitons, Springer, Berlin (1980).

    Google Scholar 

  2. SatoM. and SatoY., in H.Fujita, P. D.Lax and G.Strang, (eds.), Nonlinear Partial Differential Equations in Applied Science, Kinokuniya/North Holland, Tokyo (1983).

    Google Scholar 

  3. DateE., KashiwaraM., JimboM., and MiwaT., in M.Jimbo and T.Miwa (eds.), Nonlinear Integrable Systems — Classical Theory and Quantum Theory, World Scientific, Singapore (1983).

    Google Scholar 

  4. OhtaY., SatsumaJ., TakahashiD., and TokihiroT., Prog. Theor. Phys. Suppl. 94, 210 (1988).

    Google Scholar 

  5. SatsumaJ. and HirotaR., J. Phys. Jpn. 51, 3390 (1982).

    Google Scholar 

  6. FokasA. S., Stud. Appl. Math. 77, 253 (1987).

    Google Scholar 

  7. ManinY. I., J. Soviet Math. 11, 1 (1979).

    Google Scholar 

  8. AdlerM., Invent. Math. 50, 219 (1979).

    Google Scholar 

  9. KupershmidtB. A., Comm. Math. Phys. 99, 51 (1985).

    Google Scholar 

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Authors and Affiliations

  1. Fachbereich 17-Mathematik, GH-Universitaet Kassel, Nora-Platiel-Str.1, 3500, Kassel, West Germany

    Walter Strampp

  2. Fachbereich 17-Mathematik/Informatik, GH-Universitaet Paderborn, Warburger Str.100, 4790, Paderborn, West Germany

    Walter Oevel

Authors
  1. Walter Strampp
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  2. Walter Oevel
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Strampp, W., Oevel, W. Recursion operators and Hamiltonian structures in Sato's theory. Lett Math Phys 20, 195–210 (1990). https://doi.org/10.1007/BF00398363

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  • DOI: https://doi.org/10.1007/BF00398363

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