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Whitham deformations of top-like integrable dynamical systems

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References

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

    Google Scholar 

  2. B. A. Dubrovin, I. M. Krichever, and S. P. Novikov, “Integrable systems, I,” in: Modern Problems in Mathematics. Fundamental Trends of Investigation. Vol. 4, VINITI, Moscow, 179–284 (1985).

    Google Scholar 

  3. S. V. Manakov. “A remark on the integrability of Euler's equations of dynamics of ann-dimensional solid,” Funkts. Anal. Prilozhen.,10, No. 4, 93–94 (1976).

    Google Scholar 

  4. A. I. Bobenko, A. G. Reyman, and M. A. Semenov-Tian-Shansky, “The Kovalewski top 99 years later: A Lax pair, generalizations and explicit solutions,” Comm. Math. Phys.,122, 321–354 (1989).

    Google Scholar 

  5. H. Flaschka, M. G. Forest, and D. McLaughlin, “Multiphase averaging and the inverse scattering solutions of KdV,” Comm. Pure Appl. Math.,33, No. 6, 739–784 (1980).

    Google Scholar 

  6. A. I. Bobenko, “Integration of classical tops by the inverse scattering problem method,” Preprint, LOMI, Leningrad, 10–87 (1987).

    Google Scholar 

  7. J. D. Fay, “Theta functions on Riemann surfaces,” Lect. Notes Math.,352, Springer-Verlag, New York (1973).

    Google Scholar 

  8. R. F. Bikbaev and V. Yu. Novokshenov, “Self-similar solutions of the Whitham equations and the KdV equation with finite-gap boundary conditions,” Proc. III Intern. Kiev Workshop, Vol. 1, 32–35 (1988).

    Google Scholar 

  9. C. D. Levermore, “Hyperbolic structure of the KdV zero dispersion limit,” Comm. Partial Differential Equations,13, No. 4, 495–511 (1988).

    Google Scholar 

  10. R. F. Bikbaev, “Whitham restructuring and time asymptotics of a solution to the nonlinear Schrödinger equation with finite-gap behavior forx → ±∞, Algebra Analiz,2, No. 3, 131–143 (1990).

    Google Scholar 

  11. S. P. Novikov, “Quantization of finite-band potentials and nonlinear quasi-classics appearing in the nonperturbative theory of strings,” Funkts. Anal. Prilozhen.,24, No. 4, 43–53 (1990).

    Google Scholar 

  12. B. A. Dubrovin and S. P. Novikov, “Hydrodynamics of weakly deformed soliton lattices. Differential geometry and the Hamiltonian theory,” Usp. Mat. Nauk,44, No. 6, 29–98 (1989).

    Google Scholar 

  13. I. M. Krichever, “Averaging method for two-dimensional ‘integrable equations’,” Funkts. Anal. Prilozhen.,22, No. 3, 37–52 (1988).

    Google Scholar 

  14. S. P. Tsarev, “Poisson brackets and one-dimensional systems of hydrodynamic type,” Dokl. Akad. Nauk SSSR,282, No. 3, 534–537 (1985).

    Google Scholar 

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Authors
  1. V. Yu. Novokshenov
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Institute of Mathematics, The Urals Division of the Russian Academy of Sciences, Ufa. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 27, No. 2, pp. 50–62, April–June, 1993.

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Novokshenov, V.Y. Whitham deformations of top-like integrable dynamical systems. Funct Anal Its Appl 27, 118–127 (1993). https://doi.org/10.1007/BF01085982

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