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TMF, 1998, Volume 115, Number 3, Pages 323–348 (Mi tmf877)  

This article is cited in 4 scientific papers (total in 4 papers)

Nonlinear $\sigma$-model in a curved space, gauge equivalence, and exact solutions of $(2+0)$-dimensional integrable equations

E. Sh. Gutshabasha, V. D. Lipovskii, S. S. Nikulichev

a V. A. Fock Institute of Physics, Saint-Petersburg State University

Abstract: We propose a nonlinear $\sigma$-model in a curved space as a general integrable elliptic model. We construct its exact solutions and obtain energy estimates near the critical point. We consider the Pohlmeyer transformation in Euclidean space and investigate the gauge equivalence conditions for a broad class of elliptic equations. We develop the inverse scattering transform method for the $\operatorname {sh}$-Gordon equation and evaluate its exact and asymptotic solutions.

DOI: https://doi.org/10.4213/tmf877

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English version:
Theoretical and Mathematical Physics, 1998, 115:3, 619–638

Bibliographic databases:

Received: 14.01.1998

Citation: E. Sh. Gutshabash, V. D. Lipovskii, S. S. Nikulichev, “Nonlinear $\sigma$-model in a curved space, gauge equivalence, and exact solutions of $(2+0)$-dimensional integrable equations”, TMF, 115:3 (1998), 323–348; Theoret. and Math. Phys., 115:3 (1998), 619–638

Citation in format AMSBIB
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\by E.~Sh.~Gutshabash, V.~D.~Lipovskii, S.~S.~Nikulichev
\paper Nonlinear $\sigma$-model in a curved space, gauge equivalence, and exact solutions of
$(2+0)$-dimensional integrable equations
\jour TMF
\yr 1998
\vol 115
\issue 3
\pages 323--348
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\zmath{https://zbmath.org/?q=an:1113.81095}
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\transl
\jour Theoret. and Math. Phys.
\yr 1998
\vol 115
\issue 3
\pages 619--638
\crossref{https://doi.org/10.1007/BF02575486}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Pritula, GM, “Stationary structures in two-dimensional continuous Heisenberg ferromagnetic spin system”, Journal of Nonlinear Mathematical Physics, 10:3 (2003), 256  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    2. E. Sh. Gutshabash, “Hydrodynamical vortice on the plain”, J. Math. Sci. (N. Y.), 143:1 (2007), 2765–2772  mathnet  crossref  mathscinet  zmath
    3. Mehrabi, AR, “ANALYSIS AND SIMULATION OF LONG-RANGE CORRELATIONS IN CURVED SPACE”, International Journal of Modern Physics C, 20:8 (2009), 1211  crossref  zmath  adsnasa  isi  scopus  scopus  scopus
    4. E. Sh. Gutshabash, “Nonlinear sigma model, Zakharov–Shabat method, and new exact forms of the minimal surfaces in ${\mathbb R}^3$”, JETP Letters, 99:12 (2014), 715–719  mathnet  crossref  crossref  isi  elib  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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