General information
Latest issue
Impact factor
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Uspekhi Mat. Nauk:

Personal entry:
Save password
Forgotten password?

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

This article is cited in 42 scientific papers (total in 42 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)
References: PDF file   HTML file

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
\by E.~D.~Belokolos, A.~I.~Bobenko, V.~B.~Matveev, V.~Z.~\`Enol'skii
\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
\jour Russian Math. Surveys
\yr 1986
\vol 41
\issue 2
\pages 1--49

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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
    10. A. I. Bobenko, “Constant mean curvature surfaces and integrable equations”, Russian Math. Surveys, 46:4 (1991), 1–45  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    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
    17. F. Gesztesy, R. Weikard, “Treibich-Verdier potentials and the stationary (m)KdV hierarchy”, Math Z, 219:1 (1995), 451  crossref  mathscinet  zmath  isi
    18. F. Gesztesy, R. Weikard, “Lamé Potentials and the Stationary (m)KdV Hierarchy”, Math Nachr, 176:1 (1995), 73  crossref  mathscinet  zmath  isi
    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
    21. Fritz Gesztesy, Rudi Weikard, “Picard potentials and Hill's equation on a torus”, Acta Math, 176:1 (1996), 73  crossref  mathscinet  zmath  isi
    22. 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
    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
    27. 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
    28. Fritz Gesztesy, Rudi Weikard, “A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy”, Acta Math, 181:1 (1998), 63  crossref  mathscinet  zmath  isi
    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
    31. 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
    32. Thérèse Falliero, Ahmed Sebbar, “Capacité d'une union de trois intervalles et fonctions thêta de genre 2”, Journal de Mathématiques Pures et Appliquées, 80:4 (2001), 409  crossref
    33. Yu. N. Sirota, A. O. Smirnov, “The Heun Equation and the Darboux Transformation”, Math. Notes, 79:2 (2006), 244–253  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    34. Accola, RDM, “Covers of tori: Genus two”, Letters in Mathematical Physics, 76:2–3 (2006), 135  crossref  mathscinet  zmath  adsnasa  isi  elib
    35. Gesztesy, F, “An explicit characterization of Calogero–Moser systems”, Transactions of the American Mathematical Society, 358:2 (2006), 603  crossref  mathscinet  zmath  isi  elib
    36. Matveev, VB, “30 years of finite-gap integration theory”, Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 366:1867 (2008), 837  crossref  mathscinet  zmath  adsnasa  isi  elib
    37. Maier, RS, “Lame polynomials, hyperelliptic reductions and Lame band structure”, Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 366:1867 (2008), 1115  crossref  mathscinet  zmath  adsnasa  isi
    38. Alisher Yakhshimuratov, “The Nonlinear Schrödinger Equation with a Self-consistent Source in the Class of Periodic Functions”, Math Phys Anal Geom, 2011  crossref
    39. A. O. Smirnov, G. M. Golovachev, E. G. Amosenok, “Dvukhzonnye 3-ellipticheskie resheniya uravnenii Bussineska i Kortevega–de Friza”, Nelineinaya dinam., 7:2 (2011), 239–256  mathnet  elib
    40. Giovanni Mingari Scarpello, Daniele Ritelli, “On computing some special values of multivariate hypergeometric functions”, Journal of Mathematical Analysis and Applications, 2014  crossref
    41. R. F. Bikbaev, A. I. Bobenko, A. R. Its, “Landau–Lifshitz equation, uniaxial anisotropy case: Theory of exact solutions”, Theoret. and Math. Phys., 178:2 (2014), 143–193  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    42. A. B. Yakhshimuratov, “Integration of a higher-order nonlinear Schrödinger system with a self-consistent source in the class of periodic functions”, Theoret. and Math. Phys., 202:2 (2020), 137–149  mathnet  crossref  crossref  isi  elib
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:837
    Full text:272
    First page:2

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020