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

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Teoreticheskaya i Matematicheskaya Fizika, 1998, Volume 115, Number 3, Pages 323–348
DOI: https://doi.org/10.4213/tmf877 (Mi tmf877)

This article is cited in 5 scientific papers (total in 5 papers)

Nonlinear

σ

$\sigma$ -model in a curved space, gauge equivalence, and exact solutions of

(2 + 0)

$(2+0)$ -dimensional integrable equations

E. Sh. Gutshabash^a, V. D. Lipovskii, S. S. Nikulichev

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

Full-text PDF (331 kB) Citations (5)

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

Abstract: We propose a nonlinear

σ

$\sigma$ -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

sh

$\operatorname {sh}$ -Gordon equation and evaluate its exact and asymptotic solutions.

Received: 14.01.1998

English version:
Theoretical and Mathematical Physics, 1998, Volume 115, Issue 3, Pages 619–638
DOI: https://doi.org/10.1007/BF02575486

Bibliographic databases:

Language: Russian

Citation: E. Sh. Gutshabash, V. D. Lipovskii, S. S. Nikulichev, “Nonlinear

σ

$\sigma$ -model in a curved space, gauge equivalence, and exact solutions of

(2 + 0)

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

$(2+0)$-dimensional integrable equations

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\pages 323--348

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\transl

\jour Theoret. and Math. Phys.

\yr 1998

\vol 115

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\crossref{https://doi.org/10.1007/BF02575486}

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Linking options:

https://www.mathnet.ru/eng/tmf877

https://doi.org/10.4213/tmf877

https://www.mathnet.ru/eng/tmf/v115/i3/p323

This publication is cited in the following 5 articles:

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
Mehrabi, AR, “ANALYSIS AND SIMULATION OF LONG-RANGE CORRELATIONS IN CURVED SPACE”, International Journal of Modern Physics C, 20:8 (2009), 1211
E. Sh. Gutshabash, “Hydrodynamical vortice on the plain”, J. Math. Sci. (N. Y.), 143:1 (2007), 2765–2772
Pritula, GM, “Stationary structures in two-dimensional continuous Heisenberg ferromagnetic spin system”, Journal of Nonlinear Mathematical Physics, 10:3 (2003), 256
E.Sh. Gutshabash, International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367), 1999, 48

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

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References:	75
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