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Prog. Theor. Phys. Vol. 80 No. 5 (1988) pp. 749-751

[ Full Text PDF : FREE ACCESS (91K) ]

Letters

Integrals of a Lotka-Volterra System of Infinite Species

Yoshiaki Itoh

The Institute of Statistical Mathematics, Minami-Azabu, Tokyo 106

(Received July 15, 1988)

Abstract:

A Lotka-Volterra system of infinite species is introduced. Each of the infinite species is represented by a point on a unit circle. The probability density on the circle is given by the solution of the Lotka-Volterra system. Infinite number of conserved quantities are given for the system.


URL : http://ptp.ipap.jp/link?PTP/80/749/
DOI : 10.1143/PTP.80.749

[ Full Text PDF : FREE ACCESS (91K) ] Citation:

References:

  1. Y. Itoh, Prog. Theor. Phys. 78 (1987), 507[PTP].
  2. J. Moser, Adv. in Math. 16 (1975), 197.
  3. R. Hirota and J. Satsuma, Prog. Theor. Phys. Suppl. No. 59 (1976), 64[PTP].
  4. M. Wadati, Prog. Theor. Phys. Suppl. No. 59 (1976), 36[PTP].
  5. M. Toda, Theory of Nonlinear Lattices (Springer, Berlin, 1981).
  6. K. Narita, J. Phys. Soc. Jpn. 51 (1982), 1682[JPSJ].
  7. M. Toda, J. Phys. Soc. Jpn. 22 (1967), 431[JPSJ].
  8. M. Henon, Phys. Rev. B9 (1974), 1921[APS].
  9. H. Flaschka, Phys. Rev. B9 (1974), 1924[APS].
  10. K. Sawada and T. Kotera, Prog. Theor. Phys. Suppl. No. 59 (1976), 101[PTP].
  11. Y. Itoh, Ann. Inst. Statist. Math. 25 (1973), 635.
  12. Y. Itoh, Proc. Japan Acad. 51 (1975), 374.
  13. Y. Itoh, Seminar on Probability 44 (1977), 141 (in Japanese).
  14. Y. Itoh, J. Appl. Prob. 16 (1979), 36.
  15. Y. Itoh and S. Ueda, Proc. Inst. Statist. Math. 28 (1981), 55 (in Japanese with English summary).
  16. Y. Itoh, Proc. Inst. Statist. Math. 35 (1987), 73 (in Japanese with English summary).

Citing Article(s) :

  1. Journal of the Physical Society of Japan 62 (1993) pp. 1826-1828 :
    Stochastic Model of an Integrable Nonlinear System
    Yoshiaki Itoh
  2. Journal of the Physical Society of Japan 66 (1997) pp. 3756-3763 :
    Hidden Symmetry of the Bogoyavlensky Lattice. the Lattice W Algebras and the Vertex Operators
    Kazuhiro Hikami, Kiyoshi Sogo and Rei Inoue
  3. Journal of the Physical Society of Japan 67 (1998) pp. 3729-3733 :
    Discrete Time Bogoyavlensky Lattice and Lattice W Currents
    Rei Inoue and Kazuhiro Hikami
  4. Journal of the Physical Society of Japan 68 (1999) pp. 386-390 :
    Lattice W Currents with Discrete Time
    Rei Inoue and Kazuhiro Hikami
  5. Journal of the Physical Society of Japan 68 (1999) pp. 776-783 :
    The Hamiltonian Structure of the Bogoyavlensky Lattice
    Kazuhiro Hikami and Rei Inoue

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