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Functional Analysis and Its Applications

, Volume 14, Issue 4, pp 282–290 | Cite as

Elliptic solutions of the Kadomtsev-Petviashvili equation and integrable systems of particles

  • I. M. Krichever
Article

Keywords

Functional Analysis Integrable System Elliptic Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature Cited

  1. 1.
    H. Bateman and A. Erdelyi, Higher Transcendental Functions. Elliptic and Automorphic Functions, Lamé and Mathieu Functions [Russian translation], Nauka, Moscow (1967).Google Scholar
  2. 2.
    F. Calogero, "Exactly solvable one-dimensional many-body systems," Lett. Nuovo Cimento,13, 411–415 (1975).Google Scholar
  3. 3.
    A. M. Perelomov, "Completely integrable classical systems connected with semisimple Lie algebras," Lett. Math. Phys.,1, 531–540 (1977).Google Scholar
  4. 4.
    H. Airault, H. McKean, and J. Moser, "Rational and elliptic solutions of the KdV equation and related many-body problem," Commun. Pure Appl. Math.,30, 95–125 (1977).Google Scholar
  5. 5.
    I. M. Krichever, "Rational solutions of the Kadomtsev—Petviashvili equation and integrable systems of N particles on a line," Funkts. Anal. Prilozhen.,12, No. 1, 76–78 (1978).Google Scholar
  6. 6.
    D. V. Choodnovsky and G. V. Choodnovsky, "Pole expansions of nonlinear partial differential equations," Nuovo Cimento,40B, 339–350 (1977).Google Scholar
  7. 7.
    F. Calogero, "Integrable many-body problem," Preprint, Univ. di Roma, No. 89 (1978).Google Scholar
  8. 8.
    K. M. Case, "The N-soliton solutions of the Bendgamine—Ono equation," Proc. Nat. Acad. Sci. USA,75, 3562–3563 (1978).Google Scholar
  9. 9.
    M. A. Olshanetsky and A. M. Perelomov, "Explicit solutions of some completely integrable systems," Lett. Nuovo Cimento,17, 97–133 (1976).Google Scholar
  10. 10.
    M. A. Olshanetsky and N. V. Rogov, "Bound states in completely integrable systems with two types of particles," Ann. Inst. H. Poincare,29, 169–177 (1978).Google Scholar
  11. 11.
    D. V. Choodnovsky, "Meromorphic solutions of nonlinear partial differential equations and particle integrable systems," J. Math. Phys.,20, No. 12, 2416–2424 (1979).Google Scholar
  12. 12.
    V. S. Dryuma, "An analytic solution of the two-dimensional Korteweg—de Vries equation," Pis'ma Zh. Eksp. Teor. Fiz.,19, No. 12, 219–225 (1973).Google Scholar
  13. 13.
    V. E. Zakharov and A. B. Shabat, "A scheme for the integration of nonlinear equations of mathematical physics by an inverse problem of scattering theory. I," Funkts. Anal. Prilozhen.,8, No. 3, 43–53 (1974).Google Scholar
  14. 14.
    E. Kamke, Handbook on Ordinary Differential Equations [in German], Chelsea Publ.Google Scholar
  15. 15.
    I. M. Krichever, "An algebraic-geometric construction of the Zakharov—Shabat equations and their periodic solutions," Dokl. Akad. Nauk SSSR,227, No. 2, 291–294 (1976).Google Scholar
  16. 16.
    I. M. Krichever, "The integration of nonlinear equations by the methods of algebraic geometry," Funkts. Anal. Prilozhen.,11, No. 1, 15–31 (1977).Google Scholar
  17. 17.
    H. Baker, "Note on the foregoing paper, ‘Commutative ordinary differential equations,’" Proc. R. Soc. London, Ser. A,118, 570–576 (1928).Google Scholar
  18. 18.
    B. A. Dubrovin and S. P. Novikov, "Periodic and conditionally periodic analogues of many-soliton solutions of the Korteweg—de Vries equation," Zh. Eksp. Teor. Fiz.,67, No. 12, 2131–2143 (1974).Google Scholar

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© Plenum Publishing Corporation 1981

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  • I. M. Krichever

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