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Funktsional. Anal. i Prilozhen., 1980, Volume 14, Issue 4, Pages 45–54 (Mi faa1852)  

This article is cited in 72 scientific papers (total in 72 papers)

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

I. M. Krichever

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English version:
Functional Analysis and Its Applications, 1980, 14:4, 282–290

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UDC: 517.9
Received: 11.03.1980

Citation: I. M. Krichever, “Elliptic solutions of the Kadomtsev–Petviashvili equation and integrable systems of particles”, Funktsional. Anal. i Prilozhen., 14:4 (1980), 45–54; Funct. Anal. Appl., 14:4 (1980), 282–290

Citation in format AMSBIB
\by I.~M.~Krichever
\paper Elliptic solutions of the Kadomtsev--Petviashvili equation and integrable systems of particles
\jour Funktsional. Anal. i Prilozhen.
\yr 1980
\vol 14
\issue 4
\pages 45--54
\jour Funct. Anal. Appl.
\yr 1980
\vol 14
\issue 4
\pages 282--290

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    2. E. D. Belokolos, V. Z. Ènol'skii, “Generalized Lamb ansatz”, Theoret. and Math. Phys., 53:2 (1982), 1120–1127  mathnet  crossref  mathscinet  zmath  isi
    3. M. V. Babich, A. I. Bobenko, V. B. Matveev, “Solutions of nonlinear equations integrable in Jacobi theta functions by the method of the inverse problem, and symmetries of algebraic curves”, Math. USSR-Izv., 26:3 (1986), 479–496  mathnet  crossref  mathscinet  zmath
    4. A. R. Its, V. Z. Ènol'skii, “Dynamics of the Calogero–Moser system and the reduction of hyperelliptic integrals to elliptic integrals”, Funct. Anal. Appl., 20:1 (1986), 62–64  mathnet  crossref  mathscinet  zmath  isi
    5. A. O. Smirnov, “Finite-gap solutions of Abelian Toda chain of genus 4 and 5 in elliptic functions”, Theoret. and Math. Phys., 78:1 (1989), 6–13  mathnet  crossref  mathscinet  isi
    6. A. O. Smirnov, “Real elliptic solutions of the “sine-Gordon” equation”, Math. USSR-Sb., 70:1 (1991), 231–240  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. V. M. Buchstaber, “Functional equations associated with addition theorems for elliptic functions and two-valued algebraic groups”, Russian Math. Surveys, 45:3 (1990), 213–215  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. I. A. Taimanov, “Elliptic solutions of nonlinear equations”, Theoret. and Math. Phys., 84:1 (1990), 700–706  mathnet  crossref  mathscinet  zmath  isi
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    10. A. O. Smirnov, “Elliptic solutions of the nonlinear Schrödinger equation and the modified Korteweg–de Vries equation”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 461–470  mathnet  crossref  mathscinet  zmath  isi
    11. A. O. Smirnov, “Solutions of the KdV equation elliptic in $t$”, Theoret. and Math. Phys., 100:2 (1994), 937–947  mathnet  crossref  mathscinet  zmath  isi
    12. A. P. Veselov, “Calogero quantum problem, Knizhnik–Zamolodchikov equation and Huygens principle”, Theoret. and Math. Phys., 98:3 (1994), 368–376  mathnet  crossref  mathscinet  zmath  isi
    13. Theoret. and Math. Phys., 103:3 (1995), 681–700  mathnet  crossref  mathscinet  zmath  isi
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    15. A. O. Smirnov, “The Dirac operator with elliptic potential”, Sb. Math., 186:8 (1995), 1213–1221  mathnet  crossref  mathscinet  zmath  isi
    16. A. O. Smirnov, “Elliptic in $t$ solutions of the nonlinear Schrödinger equation”, Theoret. and Math. Phys., 107:2 (1996), 568–578  mathnet  crossref  crossref  mathscinet  zmath  isi
    17. A. O. Smirnov, “On some set of elliptic solutions of the Boussinesq equation”, Theoret. and Math. Phys., 109:3 (1996), 1515–1522  mathnet  crossref  crossref  mathscinet  zmath  isi
    18. A. O. Smirnov, “On a class of elliptic potentials of the Dirac operator”, Sb. Math., 188:1 (1997), 115–135  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    19. A. V. Marshakov, “On integrable systems and supersymmetric gauge theories”, Theoret. and Math. Phys., 112:1 (1997), 791–826  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    20. A. V. Marshakov, “Strings, SUSY gauge theories, and integrable systems”, Theoret. and Math. Phys., 121:2 (1999), 1409–1461  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    21. A. O. Smirnov, “Two-gap elliptic solutions of the Boussinesq equation”, Sb. Math., 190:5 (1999), 763–781  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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    23. A. Treibich, “Hyperelliptic tangential covers and finite-gap potentials”, Russian Math. Surveys, 56:6 (2001), 1107–1151  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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    25. Eilbeck, JC, “Varieties of elliptic solitons”, Journal of Physics A-Mathematical and General, 34:11 (2001), 2215  crossref  isi
    26. Treibich, A, “Difference analogs of elliptic KdV solitons and Schrodinger operators”, International Mathematics Research Notices, 2003, no. 6, 313  isi
    27. Eilbeck, JC, “On a generalized Frobenius-Stickelberger addition formula”, Letters in Mathematical Physics, 63:1 (2003), 5  crossref  isi
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    29. Fledrich, P, “Hyperelliptic osculating covers and KdV solutions periodic in tau”, International Mathematics Research Notices, 2006, 73476  isi
    30. Gesztesy, F, “An explicit characterization of Calogero–Moser systems”, Transactions of the American Mathematical Society, 358:2 (2006), 603  crossref  isi
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