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Funktsional. Anal. i Prilozhen., 1982, Volume 16, Issue 1, Pages 27–43 (Mi faa1594)  

This article is cited in 27 scientific papers (total in 27 papers)

Real two-zone solutions of the sine-Gordon equation

B. A. Dubrovin, S. M. Natanzon


Full text: PDF file (1684 kB)
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English version:
Functional Analysis and Its Applications, 1982, 16:1, 21–33

Bibliographic databases:

UDC: 517.9
Received: 10.06.1981

Citation: B. A. Dubrovin, S. M. Natanzon, “Real two-zone solutions of the sine-Gordon equation”, Funktsional. Anal. i Prilozhen., 16:1 (1982), 27–43; Funct. Anal. Appl., 16:1 (1982), 21–33

Citation in format AMSBIB
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\by B.~A.~Dubrovin, S.~M.~Natanzon
\paper Real two-zone solutions of the sine-Gordon equation
\jour Funktsional. Anal. i Prilozhen.
\yr 1982
\vol 16
\issue 1
\pages 27--43
\mathnet{http://mi.mathnet.ru/faa1594}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=648807}
\zmath{https://zbmath.org/?q=an:0554.35100}
\transl
\jour Funct. Anal. Appl.
\yr 1982
\vol 16
\issue 1
\pages 21--33
\crossref{https://doi.org/10.1007/BF01081805}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1982PM22200005}


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    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. E. D. Belokolos, V. Z. Ènol'skii, “Generalized Lamb ansatz”, Theoret. and Math. Phys., 53:2 (1982), 1120–1127  mathnet  crossref  mathscinet  zmath  isi
    2. A. I. Bobenko, “Periodic finite-zone solutions of the sine-Gordon equation”, Funct. Anal. Appl., 18:3 (1984), 240–242  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. R. F. Bikbaev, “Finite-gap solutions of the massive Thirring model”, Theoret. and Math. Phys., 63:3 (1985), 577–584  mathnet  crossref  mathscinet  isi
    5. A. I. Bobenko, “Real algebrogeometric solutions of the Landau–Lifshits equation in prym theta functions”, Funct. Anal. Appl., 19:1 (1985), 5–17  mathnet  crossref  mathscinet  zmath  isi
    6. 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
    7. 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”, Russian Math. Surveys, 41:2 (1986), 1–49  mathnet  crossref  mathscinet  zmath  isi
    8. R. A. Sharipov, “Multiplet solutions of the Kadomtsev–Petviashvili equation against a finite-zone background”, Russian Math. Surveys, 42:5 (1987), 177–178  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. A. O. Smirnov, “A matrix analogue of Appell's theorem and reductions of multidimensional Riemann theta-functions”, Math. USSR-Sb., 61:2 (1988), 379–388  mathnet  crossref  mathscinet  zmath
    10. B. A. Dubrovin, S. M. Natanzon, “Real theta-function solutions of the Kadomtsev–Petviashvili equation”, Math. USSR-Izv., 32:2 (1989), 269–288  mathnet  crossref  mathscinet  zmath
    11. S. M. Natanzon, “Prymians of real curves and their applications to the effectivization of Schrödinger operators”, Funct. Anal. Appl., 23:1 (1989), 33–45  mathnet  crossref  mathscinet  zmath  isi
    12. 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
    13. S. M. Natanzon, “Klein surfaces”, Russian Math. Surveys, 45:5 (1990), 53–108  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. I. A. Taimanov, “Elliptic solutions of nonlinear equations”, Theoret. and Math. Phys., 84:1 (1990), 700–706  mathnet  crossref  mathscinet  zmath  isi
    15. A. I. Bobenko, “Constant mean curvature surfaces and integrable equations”, Russian Math. Surveys, 46:4 (1991), 1–45  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. A. O. Smirnov, “Two-gap elliptic solutions to integrable nonlinear equations”, Math. Notes, 58:1 (1995), 735–743  mathnet  crossref  mathscinet  zmath  isi
    17. V. Yu. Novokshenov, “Whitham Gap Dynamics of the Real-Valued Solution of the Sine-Gordon Equation with Finite-Gap Boundary Conditions”, Funct. Anal. Appl., 30:4 (1996), 246–256  mathnet  crossref  crossref  mathscinet  zmath  isi
    18. A. O. Smirnov, “3-Elliptic solutions of the sine-Gordon equation”, Math. Notes, 62:3 (1997), 368–376  mathnet  crossref  crossref  mathscinet  zmath  isi
    19. 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
    20. S. M. Natanzon, “Moduli of real algebraic surfaces, and their superanalogues. Differentials, spinors, and Jacobians of real curves”, Russian Math. Surveys, 54:6 (1999), 1091–1147  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    21. R. K. Romanovskii, S. G. Sadovnichuk, “A direct method of construction of two-zone solutions of nonlinear equations”, Math. Notes, 66:3 (1999), 323–327  mathnet  crossref  crossref  mathscinet  zmath  isi
    22. P. G. Grinevich, S. P. Novikov, “Real finite-zone solutions of the sine-Gordon equation: a formula for the topological charge”, Russian Math. Surveys, 56:5 (2001), 980–981  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    23. Yu. V. Brezhnev, “Finite-Band Potentials with Trigonal Curves”, Theoret. and Math. Phys., 133:3 (2002), 1657–1662  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    24. P. G. Grinevich, K. V. Kaipa, “Multiscale Limit for Finite-Gap Sine-Gordon Solutions and Calculation of Topological Charge Using Theta-Functional Formulae”, Proc. Steklov Inst. Math., 266 (2009), 49–58  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    25. Treibich A., “Nonlinear evolution equations and hyperelliptic covers of elliptic curves”, Regular & Chaotic Dynamics, 16:3–4 (2011), 290–310  crossref  isi
    26. 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
    27. Oganesyan V., “Matrix Commuting Differential Operators of Rank 2 and Arbitrary Genus”, Int. Math. Res. Notices, 2019, no. 3, 834–851  crossref  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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