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

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Teoreticheskaya i Matematicheskaya Fizika, 2015, Volume 182, Number 2, Pages 213–222
DOI: https://doi.org/10.4213/tmf8785 (Mi tmf8785)

This article is cited in 14 scientific papers (total in 14 papers)

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

I. A. Taimanov^ab

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

Full-text PDF (409 kB) Citations (14)

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

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

Received: 27.08.2014

English version:
Theoretical and Mathematical Physics, 2015, Volume 182, Issue 2, Pages 173–181
DOI: https://doi.org/10.1007/s11232-015-0255-5

Bibliographic databases:

Document Type: Article

Language: Russian

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

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https://doi.org/10.4213/tmf8785

https://www.mathnet.ru/eng/tmf/v182/i2/p213

This publication is cited in the following 14 articles:

Iskander A. Taimanov, “On a Formation of Singularities of Solutions to Soliton Equations Represented by L, A, B-triples”, Acta. Math. Sin.-English Ser., 40:1 (2024), 406
P. G. Grinevich, “Riemann Surfaces Close to Degenerate Ones in the Theory of Rogue Waves”, Proc. Steklov Inst. Math., 325 (2024), 86–110
P. G. Grinevich, P. M. Santini, “The finite-gap method and the periodic Cauchy problem for $(2+1)$ -dimensional anomalous waves for the focusing Davey–Stewartson $2$ equation”, Russian Math. Surveys, 77:6 (2022), 1029–1059
I. A. Taimanov, “The Moutard Transformation for the Davey–Stewartson II Equation and Its Geometrical Meaning”, Math. Notes, 110:5 (2021), 754–766
P. G. Grinevich, R. G. Novikov, “Creation and annihilation of point-potentials using Moutard-type transform in spectral variable”, J. Math. Phys., 61:9 (2020), 093501
A. A. Yurova, A. V. Yurov, V. A. Yurov, “The Cauchy problem for the generalized hyperbolic Novikov-Veselov equation via the Moutard symmetries”, Symmetry-Basel, 12:12 (2020), 2113
Damir Kurmanbayev, “Exact Solution of Modified Veselov–Novikov Equation and Some Applications in the Game Theory”, International Journal of Mathematics and Mathematical Sciences, 2020 (2020), 1
P. G. Grinevich, R. G. Novikov, “Moutard transforms for the conductivity equation”, Lett. Math. Phys., 109:10 (2019), 2209–2222
R. G. Novikov, I. A. Taimanov, “Darboux–Moutard transformations and Poincaré–Steklov operators”, Proc. Steklov Inst. Math., 302 (2018), 315–324
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
P. G. Grinevich, S. P. Novikov, “Singular solitons and spectral meromorphy”, Russian Math. Surveys, 72:6 (2017), 1083–1107
P. G. Grinevich, R. G. Novikov, “Generalized Analytic Functions, Moutard-Type Transforms, and Holomorphic Maps”, Funct. Anal. Appl., 50:2 (2016), 150–152
P. G. Grinevich, R. G. Novikov, “Moutard transform for generalized analytic functions”, J. Geom. Anal., 26:4 (2016), 2984–2995
P. G. Grinevich, R. G. Novikov, “Moutard transform approach to generalized analytic functions with contour poles”, Bull. Sci. Math., 140:6 (2016), 638–656

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

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