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TMF, 1987, Volume 70, Number 2, Pages 309–314 (Mi tmf4647)  

This article is cited in 17 scientific papers (total in 17 papers)

Veselov–Novikov equation as a natural two-dimensional generalization of the Korteweg–de Vries equation

L. V. Bogdanov


Abstract: Miura transform between the solutions of KdF and MKdF equations is extended to the two-dimensional case. An integrable equation connected with the two-dimensional Dirac operator – modified Vesselov–Novikov equation – is introduced.

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English version:
Theoretical and Mathematical Physics, 1987, 70:2, 219–223

Bibliographic databases:

Received: 28.01.1986

Citation: L. V. Bogdanov, “Veselov–Novikov equation as a natural two-dimensional generalization of the Korteweg–de Vries equation”, TMF, 70:2 (1987), 309–314; Theoret. and Math. Phys., 70:2 (1987), 219–223

Citation in format AMSBIB
\Bibitem{Bog87}
\by L.~V.~Bogdanov
\paper Veselov--Novikov equation as a~natural two-dimensional generalization of the Korteweg--de~Vries equation
\jour TMF
\yr 1987
\vol 70
\issue 2
\pages 309--314
\mathnet{http://mi.mathnet.ru/tmf4647}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=894472}
\zmath{https://zbmath.org/?q=an:0639.35072}
\transl
\jour Theoret. and Math. Phys.
\yr 1987
\vol 70
\issue 2
\pages 219--223
\crossref{https://doi.org/10.1007/BF01039213}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1987K225600015}


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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. L. V. Bogdanov, “On the two-dimensional Zakharov–Shabat problem”, Theoret. and Math. Phys., 72:1 (1987), 790–793  mathnet  crossref  mathscinet  zmath  isi
    2. L. V. Ryzhik, E. I. Shulman, “Symmetry algebra of nonlinear integrable equations”, Theoret. and Math. Phys., 95:1 (1993), 387–392  mathnet  crossref  mathscinet  zmath
    3. Bogdanov, LV, “Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies”, Journal of Mathematical Physics, 39:9 (1998), 4701  crossref  isi
    4. Grinevich, PG, “Conformal invariant functionals of immersions of tori into R3”, Journal of Geometry and Physics, 26:1–2 (1998), 51  crossref  isi
    5. R. Myrzakulov, A. K. Danlybaeva, G. N. Nugmanova, “Geometry and multidimensional soliton equations”, Theoret. and Math. Phys., 118:3 (1999), 347–356  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Bogdanova, LV, “Projective differential geometry of higher reductions of the two-dimensional Dirac equation”, Journal of Geometry and Physics, 52:3 (2004), 328  crossref  isi
    7. I. A. Taimanov, “Two-dimensional Dirac operator and the theory of surfaces”, Russian Math. Surveys, 61:1 (2006), 79–159  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. Wang Hong-Yan, “The Nizhnik–Veselov–Novikov equation with self-consistent sources”, Theoret. and Math. Phys., 157:1 (2008), 1474–1483  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    9. V. G. Dubrovskii, A. V. Gramolin, “Gauge-invariant description of several $(2+1)$-dimensional integrable nonlinear evolution equations”, Theoret. and Math. Phys., 160:1 (2009), 905–916  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    10. Ferapontov, EV, “Integrable equations in 2+1 dimensions: deformations of dispersionless limits”, Journal of Physics A-Mathematical and Theoretical, 42:34 (2009), 345205  crossref  isi
    11. Chang J.-H., “The Gould-Hopper polynomials in the Novikov-Veselov equation”, J Math Phys, 52:9 (2011), 092703  crossref  isi
    12. Jen-Hsu Chang, “On the $N$-Solitons Solutions in the Novikov–Veselov Equation”, SIGMA, 9 (2013), 006, 13 pp.  mathnet  crossref  mathscinet
    13. Jen-Hsu Chang, “Mach-Type Soliton in the Novikov–Veselov Equation”, SIGMA, 10 (2014), 111, 14 pp.  mathnet  crossref
    14. Perry P.A., “Miura Maps and Inverse Scattering For the Novikov-Veselov Equation”, Anal. PDE, 7:2 (2014), 311–343  crossref  isi
    15. I. A. Taimanov, “The Moutard Transformation of Two-Dimensional Dirac Operators and Möbius Geometry”, Math. Notes, 97:1 (2015), 124–135  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. I. A. Taimanov, “Blowing up solutions of the modified Novikov–Veselov equation and minimal surfaces”, Theoret. and Math. Phys., 182:2 (2015), 173–181  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    17. Chang J.-H., “The interactions of solitons in the Novikov–Veselov equation”, Appl. Anal., 95:6 (2016), 1370–1388  crossref  mathscinet  zmath  isi  elib  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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