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TMF, 1982, Volume 53, Number 2, Pages 271–282 (Mi tmf4381)  

This article is cited in 13 scientific papers (total in 13 papers)

Generalized Lamb ansatz

E. D. Belokolos, V. Z. Ènol'skii


Abstract: For the equation $\varphi_{xx}-\varphi_{tt}=\sin\varphi$, a class of 2-phase solutions is constructed. They can be expressed in terms of Jacobi theta functions and contain the Lamb ansatz as a special case. An analogous class of solutions can also be obtained for other integrable nonlinear equations that admit solutions in terms of Riemaan theta functions.

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English version:
Theoretical and Mathematical Physics, 1982, 53:2, 1120–1127

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Received: 21.10.1981

Citation: E. D. Belokolos, V. Z. Ènol'skii, “Generalized Lamb ansatz”, TMF, 53:2 (1982), 271–282; Theoret. and Math. Phys., 53:2 (1982), 1120–1127

Citation in format AMSBIB
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\by E.~D.~Belokolos, V.~Z.~\`Enol'skii
\paper Generalized Lamb ansatz
\jour TMF
\yr 1982
\vol 53
\issue 2
\pages 271--282
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=693277}
\zmath{https://zbmath.org/?q=an:0507.35060}
\transl
\jour Theoret. and Math. Phys.
\yr 1982
\vol 53
\issue 2
\pages 1120--1127
\crossref{https://doi.org/10.1007/BF01016682}
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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. 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
    2. 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
    3. 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
    4. 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
    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. I. A. Taimanov, “Elliptic solutions of nonlinear equations”, Theoret. and Math. Phys., 84:1 (1990), 700–706  mathnet  crossref  mathscinet  zmath  isi
    8. 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
    9. 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
    10. 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
    11. A. O. Smirnov, “3-Elliptic solutions of the sine-Gordon equation”, Math. Notes, 62:3 (1997), 368–376  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. 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
    13. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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