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Hamiltonian structure of the integrable equations under matrix Z N-reduction

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Abstract

The general form of the integrable equations under matrix Z N-reduction and the corresponding infinite family of Hamiltonian structures are found.

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References

  1. GardnerC.S., J. Math. Phys. 12, 1548 (1971).

    Google Scholar 

  2. ZakharovV.E. and FaddeevL.D., Funct. Anal. Appl. 5, No. 4, 18 (1971) (in Russian).

    Google Scholar 

  3. FlaschkaH. and NewellA.C., Lecture Notes in Physics, 38, 355 (1975).

    Google Scholar 

  4. GelfandI.M. and DikijL.A., Funct. Anal. Appl. 11, No. 2, 11 (1977); No. 2, 8 (1978) (in Russian).

    Google Scholar 

  5. ZakharovV.E., ManakovS.V., NovikovS.P., and PitaevskiL.P., Soliton Theory. Method of the Inverse Problem, Nauka, Moscow, 1980 (in Russian).

    Book  MathSciNet  MATH  Google Scholar 

  6. MikhailovA.V., Pisma ZhETF, 30 443 (1979) (in Russian).

    Google Scholar 

  7. Mikhailov, A.V., in ‘Proc. of Soviet-American Symposium on Soliton Theory’, September 1979, Kiev, Physica 3D, 73 (1981).

  8. FordyA.P. and GibbonsJ., Comm. Math. Phys. 77, 21 (1980).

    Google Scholar 

  9. FordyA.P. and GibbonsJ., J. Math. Phys. 21, 2508 (1980); 22, 1170 (1981).

    Article  Google Scholar 

  10. KupershmidtB.A. and WilsonG., Comm. Math. Phys. 81, 189 (1981).

    Google Scholar 

  11. SokolovV.V. and ShabatA.B., Funct. Anal. Appl. 14 No. 2, 79 (1980) (in Russian).

    Google Scholar 

  12. AblowitzM.J., KaupD.J., NewellA.C., SegurH., Stud. Appl. Math. 53, 249 (1974).

    Google Scholar 

  13. KonopelchenkoB.G., Phys. Lett. 75A, 447 (1980); 79A, 39 (1980); 100B, 254 (1981).

    Article  Google Scholar 

  14. KonopelchenkoB.G., J. Phys. A.: Math. Gen. 14, 1237 (1981).

    Article  Google Scholar 

  15. Konopelchenko, B.G., Funct. Anal. Appl. (1982) (in print); preprint Institute of Nuclear Physics, 80–223 (1980) (in Russian).

  16. BudagovA.S. and TakhtadjanL.A., Dokl. Akad. Nauk SSSR 235, 805 (1977) (in Russian).

    Google Scholar 

  17. ZakharovV.E. and MikhailovA.V., ZhETF, 74, 1953 (1978) (in Russian).

    Google Scholar 

  18. KonoplechenkoB.G. and MokhnachevV.G., J. Phys. A: Math. Gen 14, 1849 (1981).

    Article  Google Scholar 

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Konopelchenko, B.G. Hamiltonian structure of the integrable equations under matrix Z N-reduction. Lett Math Phys 6, 309–314 (1982). https://doi.org/10.1007/BF00400328

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