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TMF, 2009, Volume 160, Number 1, Pages 35–48 (Mi tmf6376)  

This article is cited in 1 scientific paper (total in 1 paper)

Gauge-invariant description of several $(2+1)$-dimensional integrable nonlinear evolution equations

V. G. Dubrovskii, A. V. Gramolin

Novosibirsk State Technical University

Abstract: We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada–Kotera and Kaup–Kuperschmidt system, the generalized system of dispersive long waves, and the Nizhnik–Veselov–Novikov system. We show how these forms imply both new and well-known two-dimensional integrable nonlinear equations: the Sawada–Kotera equation, Kaup–Kuperschmidt equation, dispersive long-wave system, Nizhnik–Veselov–Novikov equation, and modified Nizhnik–Veselov–Novikov equation. We consider Miura-type transformations between nonlinear equations in different gauges.

Keywords: Sawada–Kotera equation, Kaup–Kuperschmidt equation, generalized dispersive long-wave equation, Davey–Stewartson equation, Nizhnik–Veselov–Novikov equation

DOI: https://doi.org/10.4213/tmf6376

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English version:
Theoretical and Mathematical Physics, 2009, 160:1, 905–916

Bibliographic databases:


Citation: V. G. Dubrovskii, A. V. Gramolin, “Gauge-invariant description of several $(2+1)$-dimensional integrable nonlinear evolution equations”, TMF, 160:1 (2009), 35–48; Theoret. and Math. Phys., 160:1 (2009), 905–916

Citation in format AMSBIB
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\by V.~G.~Dubrovskii, A.~V.~Gramolin
\paper Gauge-invariant description of several $(2+1)$-dimensional integrable nonlinear evolution equations
\jour TMF
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\vol 160
\issue 1
\pages 35--48
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\crossref{https://doi.org/10.4213/tmf6376}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2603976}
\zmath{https://zbmath.org/?q=an:1179.35264}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2009TMP...160..905D}
\transl
\jour Theoret. and Math. Phys.
\yr 2009
\vol 160
\issue 1
\pages 905--916
\crossref{https://doi.org/10.1007/s11232-009-0080-9}
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  • https://doi.org/10.4213/tmf6376
  • http://mi.mathnet.ru/eng/tmf/v160/i1/p35

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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. Perry P.A., “Miura Maps and Inverse Scattering For the Novikov-Veselov Equation”, Anal. PDE, 7:2 (2014), 311–343  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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