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TMF, 2015, Volume 182, Number 2, Pages 213–222 (Mi tmf8785)  

This article is cited in 6 scientific papers (total in 6 papers)

Blowing up solutions of the modified Novikov–Veselov equation and minimal surfaces

I. A. Taimanovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: We propose a construction of blowup solutions of the modified Novikov–Veselov equation based on the Moutard transformation of the two-dimensional Dirac operators and on its geometric interpretation in terms of surface geometry. We consider an explicit example of such a solution constructed using the minimal Enneper surface.

Keywords: blowup solution, modified Novikov–Veselov equation, Moutard transformation, two-dimensional Dirac operator, Weierstrass representation of surfaces, minimal surface

Funding Agency Grant Number
Russian Science Foundation 14-11-00441


DOI: https://doi.org/10.4213/tmf8785

Full text: PDF file (409 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 182:2, 173–181

Bibliographic databases:

Received: 27.08.2014

Citation: I. A. Taimanov, “Blowing up solutions of the modified Novikov–Veselov equation and minimal surfaces”, TMF, 182:2 (2015), 213–222; Theoret. and Math. Phys., 182:2 (2015), 173–181

Citation in format AMSBIB
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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. P. G. Grinevich, R. G. Novikov, “Generalized Analytic Functions, Moutard-Type Transforms, and Holomorphic Maps”, Funct. Anal. Appl., 50:2 (2016), 150–152  mathnet  crossref  crossref  mathscinet  isi  elib
    2. P. G. Grinevich, R. G. Novikov, “Moutard transform for generalized analytic functions”, J. Geom. Anal., 26:4 (2016), 2984–2995  crossref  mathscinet  zmath  isi  scopus
    3. P. G. Grinevich, R. G. Novikov, “Moutard transform approach to generalized analytic functions with contour poles”, Bull. Sci. Math., 140:6 (2016), 638–656  crossref  mathscinet  zmath  isi  elib  scopus
    4. A. N. Adilkhanov, I. A. Taimanov, “On numerical study of the discrete spectrum of a two-dimensional Schrödinger operator with soliton potential”, Commun. Nonlinear Sci. Numer. Simul., 42 (2017), 83–92  crossref  mathscinet  isi  elib  scopus
    5. P. G. Grinevich, S. P. Novikov, “Singular solitons and spectral meromorphy”, Russian Math. Surveys, 72:6 (2017), 1083–1107  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. R. G. Novikov, I. A. Taimanov, “Darboux–Moutard transformations and Poincaré–Steklov operators”, Proc. Steklov Inst. Math., 302 (2018), 315–324  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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