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

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Literature Cited

  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. F. Calogero, "Exactly solvable one-dimensional many-body systems," Lett. Nuovo Cimento,13, 411–415 (1975).

    Google Scholar 

  3. A. M. Perelomov, "Completely integrable classical systems connected with semisimple Lie algebras," Lett. Math. Phys.,1, 531–540 (1977).

    Google Scholar 

  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. 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. D. V. Choodnovsky and G. V. Choodnovsky, "Pole expansions of nonlinear partial differential equations," Nuovo Cimento,40B, 339–350 (1977).

    Google Scholar 

  7. F. Calogero, "Integrable many-body problem," Preprint, Univ. di Roma, No. 89 (1978).

  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. M. A. Olshanetsky and A. M. Perelomov, "Explicit solutions of some completely integrable systems," Lett. Nuovo Cimento,17, 97–133 (1976).

    Google Scholar 

  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. 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. 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. 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. E. Kamke, Handbook on Ordinary Differential Equations [in German], Chelsea Publ.

  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. 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. H. Baker, "Note on the foregoing paper, ‘Commutative ordinary differential equations,’" Proc. R. Soc. London, Ser. A,118, 570–576 (1928).

    Google Scholar 

  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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G. M. Krzhizhanovskii Moscow Energy Institute. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 14, No. 4, pp. 45–54, October–December, 1980.

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Krichever, I.M. Elliptic solutions of the Kadomtsev-Petviashvili equation and integrable systems of particles. Funct Anal Its Appl 14, 282–290 (1980). https://doi.org/10.1007/BF01078304

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