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Sib. Èlektron. Mat. Izv., 2004, Volume 1, Pages 38–46 (Mi semr4)  

This article is cited in 10 scientific papers (total in 10 papers)

Research papers

Veselov-Novikov hierarchy of equations, and integrable deformations of minimal Lagrangian tori in $\mathbb CP^2$

A. E. Mironov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We associate a periodic two-dimensional Schrödinger operator to every Lagrangian torus in $\mathbb CP^2$ and define the spectral curve of a torus as the Floquet spectrum on this operator on the zero energy level. In this event minimal Lagrangian tori correspond to potential operators. We show that the Novikov–Veselov hierarchy of equations induces integrable deformations of a minimal Lagrangian torus in $\mathbb CP^2$ preserving the spectral curve.

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Bibliographic databases:

UDC: 514.752.4, 517.984
MSC: 35Q53, 53A10
Received July 26, 2004, published September 16, 2004

Citation: A. E. Mironov, “Veselov-Novikov hierarchy of equations, and integrable deformations of minimal Lagrangian tori in $\mathbb CP^2$”, Sib. Èlektron. Mat. Izv., 1 (2004), 38–46

Citation in format AMSBIB
\Bibitem{Mir04}
\by A.~E.~Mironov
\paper Veselov-Novikov hierarchy of equations, and integrable deformations of minimal Lagrangian tori in~$\mathbb CP^2$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2004
\vol 1
\pages 38--46
\mathnet{http://mi.mathnet.ru/semr4}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2132446}
\zmath{https://zbmath.org/?q=an:1082.35136}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. E. Mironov, “On a Family of Conformally Flat Minimal Lagrangian Tori in $\mathbb CP^3$”, Math. Notes, 81:3 (2007), 329–337  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. A. E. Mironov, “Relationship Between Symmetries of the Tzizeica Equation and the Novikov–Veselov Hierarchy”, Math. Notes, 82:4 (2007), 569–572  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Mironov A.E., Zuo Dafeng, “On a family of conformally flat Hamiltonian-minimal Lagrangian tori in $\mathbb{CP}^3$”, Int. Math. Res. Not. IMRN, 2008, rnn 078, 13 pp.  crossref  mathscinet  zmath  isi
    4. A. E. Mironov, “Spectral Data for Hamiltonian-Minimal Lagrangian Tori in $\mathbb C\mathrm P^2$”, Proc. Steklov Inst. Math., 263 (2008), 112–126  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    5. Chang J.-H., “The Gould-Hopper polynomials in the Novikov-Veselov equation”, J Math Phys, 52:9 (2011), 092703  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Jen-Hsu Chang, “On the $N$-Solitons Solutions in the Novikov–Veselov Equation”, SIGMA, 9 (2013), 006, 13 pp.  mathnet  crossref  mathscinet
    7. Wang J., Xu X., “Lagrangian Surfaces in the Complex Hyperquadric Q(2)”, J. Geom. Phys., 97 (2015), 61–68  crossref  mathscinet  zmath  isi  elib
    8. B. T. Saparbayeva, “On the Schrödinger operator connected with a family of Hamiltonian-minimal Lagrangian surfaces in $\mathbb CP^2$”, Siberian Math. J., 57:6 (2016), 1077–1081  mathnet  crossref  crossref  isi  elib
    9. M. S. Yermentay, “On minimal isotropic tori in $\mathbb CP^3$”, Siberian Math. J., 59:3 (2018), 415–419  mathnet  crossref  crossref  isi  elib
    10. A. A. Kazhymurat, “On a lower bound for the energy functional on a family of Hamiltonian minimal Lagrangian tori in $\mathbb CP^2$”, Siberian Math. J., 59:4 (2018), 641–647  mathnet  crossref  crossref  isi  elib
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