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Uspekhi Mat. Nauk, 1986, Volume 41, Issue 2(248), Pages 3–42 (Mi umn2026)  

This article is cited in 41 scientific papers (total in 41 papers)

Algebraic-geometric principles of superposition of finite-zone solutions of integrable non-linear equations

E. D. Belokolos, A. I. Bobenko, V. B. Matveev, V. Z. Ènol'skii


Full text: PDF file (2329 kB)
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English version:
Russian Mathematical Surveys, 1986, 41:2, 1–49

Bibliographic databases:

UDC: 517.836+517.853+517.833
MSC: 14K20, 14K25, 35Q53, 14H42, 14H30, 14H40
Received: 14.09.1984

Citation: E. D. Belokolos, A. I. Bobenko, V. B. Matveev, V. Z. Ènol'skii, “Algebraic-geometric principles of superposition of finite-zone solutions of integrable non-linear equations”, Uspekhi Mat. Nauk, 41:2(248) (1986), 3–42; Russian Math. Surveys, 41:2 (1986), 1–49

Citation in format AMSBIB
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\paper Algebraic-geometric principles of superposition of finite-zone solutions of integrable non-linear equations
\jour Uspekhi Mat. Nauk
\yr 1986
\vol 41
\issue 2(248)
\pages 3--42
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\jour Russian Math. Surveys
\yr 1986
\vol 41
\issue 2
\pages 1--49
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    This publication is cited in the following articles:
    1. A. O. Smirnov, “Real finite-gap regular solutions of the Kaup–Boussinesq equation”, Theoret. and Math. Phys., 66:1 (1986), 19–31  mathnet  crossref  mathscinet  zmath  isi
    2. A. I. Bobenko, “Euler equations in the algebras $e(3)$ and $so(4)$. Isomorphisms of integrable cases”, Funct. Anal. Appl., 20:1 (1986), 53–56  mathnet  crossref  mathscinet  zmath  isi
    3. 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
    4. B. A. Dubrovin, S. P. Novikov, “Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory”, Russian Math. Surveys, 44:6 (1989), 35–124  mathnet  crossref  mathscinet  zmath  adsnasa
    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. V. B. Matveev, A. O. Smirnov, “Some comments on the solvable chiral potts model”, Lett Math Phys, 19:3 (1990), 179  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. 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
    8. I. A. Taimanov, “Elliptic solutions of nonlinear equations”, Theoret. and Math. Phys., 84:1 (1990), 700–706  mathnet  crossref  mathscinet  zmath  isi
    9. A.R. Osborne, E. Segre, “Numerical solutions of the Korteweg-de Vries equation using the periodic scattering transform μ-representation”, Physica D: Nonlinear Phenomena, 44:3 (1990), 575  crossref
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    11. Kazumoto Iguchi, “Quasiperiodic systems without Cantor-set-like energy bands”, J Math Phys (N Y ), 33:11 (1992), 3736  crossref  mathscinet  zmath  isi
    12. Min Ho Lee, “The reduction of solutions of some integrable partial differential equations”, Computers & Mathematics with Applications, 25:8 (1993), 95  crossref
    13. I. M. Krichever, “Elliptic solutions of nonlinear integrable equations and related topics”, Acta Appl Math, 36:1-2 (1994), 7  crossref  mathscinet  zmath  isi  elib
    14. J. C. Eilbeck, V. Z. Enol’skii, “Elliptic Baker–Akhiezer functions and an application to an integrable dynamical system”, J Math Phys (N Y ), 35:3 (1994), 1192  crossref  mathscinet  zmath  adsnasa  isi
    15. 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
    16. 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
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    19. A. O. Smirnov, “Two-gap elliptic solutions to integrable nonlinear equations”, Math. Notes, 58:1 (1995), 735–743  mathnet  crossref  mathscinet  zmath  isi
    20. A. O. Smirnov, “The Dirac operator with elliptic potential”, Sb. Math., 186:8 (1995), 1213–1221  mathnet  crossref  mathscinet  zmath  isi
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    23. 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
    24. Ken Umeno, “Method of constructing exactly solvable chaos”, Phys Rev E, 55:5 (1997), 5280  crossref  isi
    25. I. A. Taimanov, “Secants of Abelian varieties, theta functions, and soliton equations”, Russian Math. Surveys, 52:1 (1997), 147–218  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    26. A. O. Smirnov, “3-Elliptic solutions of the sine-Gordon equation”, Math. Notes, 62:3 (1997), 368–376  mathnet  crossref  crossref  mathscinet  zmath  isi
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    29. D. P. Novikov, “Algebraic-geometric solutions of the Krichever–Novikov equation”, Theoret. and Math. Phys., 121:3 (1999), 1567–1573  mathnet  crossref  crossref  mathscinet  zmath  isi
    30. 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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