I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Uspekhi Mat. Nauk, 44:2(266) (1989), 121–184; Russian Math. Surveys, 44:2 (1989), 145

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Subscription
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Uspekhi Mat. Nauk, 1989, Volume 44, Issue 2(266), Pages 121–184 (Mi umn2275)

This article is cited in 71 scientific papers (total in 72 papers)

Spectral theory of two-dimensional periodic operators and its applications

I. M. Krichever

Full-text article is available

Full text: PDF file (3986 kB)

References: PDF file HTML file

English version:
Russian Mathematical Surveys, 1989, 44:2, 145–225

Bibliographic databases:

UDC: 517.93
MSC: 35Pxx, 35J10, 47A55, 37K10
Received: 13.07.1988

Citation: I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Uspekhi Mat. Nauk, 44:2(266) (1989), 121–184; Russian Math. Surveys, 44:2 (1989), 145–225

Citation in format AMSBIB

\Bibitem{Kri89}

\by I.~M.~Krichever

\paper Spectral theory of two-dimensional periodic operators and its applications

\jour Uspekhi Mat. Nauk

\yr 1989

\vol 44

\issue 2(266)

\pages 121--184

\mathnet{http://mi.mathnet.ru/umn2275}

\mathscinet{http://www.ams.org/mathscinet-getitem?mr=998363}

\zmath{https://zbmath.org/?q=an:0699.35188}

\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1989RuMaS..44..145K}

\transl

\jour Russian Math. Surveys

\yr 1989

\vol 44

\issue 2

\pages 145--225

\crossref{https://doi.org/10.1070/RM1989v044n02ABEH002044}

\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1989CM96900004}

Linking options:

http://mi.mathnet.ru/eng/umn2275

http://mi.mathnet.ru/eng/umn/v44/i2/p121

SHARE:

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:

B. A. Dubrovin, S. P. Novikov, “Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory”, Russian Math. Surveys, 44:6 (1989), 35–124
P. G. Grinevich, “Rapidly decreasing potentials on a background of finite-zone potentials and the $\partial$-problem on Riemann spaces”, Funct. Anal. Appl., 23:4 (1989), 321–322
I. A. Taimanov, “Prym varieties of branched coverings and nonlinear equations”, Math. USSR-Sb., 70:2 (1991), 367–384
P. G. Grinevich, A. Yu. Orlov, “Variations of the complex structure of Riemann surfaces by vector fields on a contour and objects of the KP theory. The Krichever–Novikov problem of the action on the Baker–Akhieser functions”, Funct. Anal. Appl., 24:1 (1991), 61–63
I. A. Taimanov, “Two-dimensional finite-zone Schrodinger potential operators”, Funct. Anal. Appl., 24:1 (1990), 76–77
F. Fucito, M. Martellini, A. Gamba, “Non-perturbative two-dimensional quantum gravity, KdV hierarchy and solutions of the string equations”, Physics Letters B, 248:1-2 (1990), 57
S. M. Natanzon, “Differential equations on the Prym theta function. a realness criterion for two-dimensional, finite-zone, potential Schrödinger operators”, Funct. Anal. Appl., 26:1 (1992), 13–20
B Dubrovin, “Integrable systems in topological field theory”, Nuclear Physics B, 379:3 (1992), 627
Otis C. Wright, “Korteweg–de vries zero dispersion limit: Through first breaking for cubic-like analytic initial data”, Comm Pure Appl Math, 46:3 (1993), 423
A. A. Gonchar, G. I. Marchuk, S. P. Novikov, “Vasilii Sergeevich Vladimirov (on his seventieth birthday)”, Russian Math. Surveys, 48:1 (1993), 201–212
V. M. Buchstaber, I. M. Krichever, “Vector addition theorems and Baker–Akhiezer functions”, Theoret. and Math. Phys., 94:2 (1993), 142–149
I. M. Krichever, “Two-Dimensional Algebraic-Geometric Operators with Self-Consistent Potentials”, Funct. Anal. Appl., 28:1 (1994), 21–32
Theoret. and Math. Phys., 99:2 (1994), 599–605
V. M. Buchstaber, V. Z. Ènol'skii, “Abelian Bloch solutions of the two-dimensional Schrödinger equation”, Russian Math. Surveys, 50:1 (1995), 195–197
A. Ya. Maltsev, M. V. Pavlov, “On Whitham's Averaging Method”, Funct. Anal. Appl., 29:1 (1995), 6–19
P.G. Grinevich, M.U. Schmidt, “Period preserving nonisospectral flows and the moduli space of periodic solutions of soliton equations”, Physica D: Nonlinear Phenomena, 87:1-4 (1995), 73
I. A. Taimanov, “Secants of Abelian varieties, theta functions, and soliton equations”, Russian Math. Surveys, 52:1 (1997), 147–218
I. A. Taimanov, “The global Weierstrass representation and its spectrum”, Russian Math. Surveys, 52:6 (1997), 1330–1332
A. V. Marshakov, “On integrable systems and supersymmetric gauge theories”, Theoret. and Math. Phys., 112:1 (1997), 791–826
Robert Carroll, Jen Hsu Chang, “The whitham equations revisited”, Applicable Analysis, 64:3-4 (1997), 343
O. M. Kiselev, “Basic Functions Associated with a Two-Dimensional Dirac System”, Funct. Anal. Appl., 32:1 (1998), 56–59
I. A. Taimanov, “The Weierstrass Representation of Closed Surfaces in $\mathbb{R}^3$”, Funct. Anal. Appl., 32:4 (1998), 258–267
E.D. Belokolos, V.Z. Enolskii, A.M. Korostil, “Two-phase nonlinear waves in the long Josephson junction”, Physica D: Nonlinear Phenomena, 116:1-2 (1998), 253
Bernard Deconinck, Harvey Segur, “The KP equation with quasiperiodic initial data”, Physica D: Nonlinear Phenomena, 123:1-4 (1998), 123
P.G. Grinevich, M.U. Schmidt, “Conformal invariant functionals of immersions of tori into 3”, Journal of Geometry and Physics, 26:1-2 (1998), 51
I Krichever, S P Novikov, Inverse Probl, 15:6 (1999), R1
O. M. Kiselev, “Asymptotic behaviour of the solution of the two-dimensional Dirac system with rapidly oscillating coefficients”, Sb. Math., 190:2 (1999), 233–254
A. Ya. Maltsev, “Conservation of Hamiltonian structures in Whitham's averaging method”, Izv. Math., 63:6 (1999), 1171–1201
Otis C. Wright, “The stationary equations of a coupled nonlinear Schrödinger system”, Physica D: Nonlinear Phenomena, 126:3-4 (1999), 275
Igor Anders, Anne Boutet de Monvel, “Asymptotic Solitons of the Johnson Equation”, Journal of Nonlinear Mathematical Physics, 7:3 (2000), 284
E V Ferapontov, D A Korotkin, V A Shramchenko, “Boyer Finley equation and systems of hydrodynamic type”, Class Quantum Grav, 19:24 (2002), L205
V. M. Buchstaber, D. V. Leikin, M. V. Pavlov, “Egorov Hydrodynamic Chains, the Chazy Equation, and $SL(2,\mathbb{C})$”, Funct. Anal. Appl., 37:4 (2003), 251–262
I. A. Taimanov, “On two-dimensional finite-gap potential Schrödinger and Dirac operators with singular spectral curves”, Siberian Math. J., 44:4 (2003), 686–694
E. V. Ferapontov, K. R. Khusnutdinova, “Hydrodynamic reductions of multidimensional dispersionless PDEs: The test for integrability”, J Math Phys (N Y ), 45:6 (2004), 2365
E V Ferapontov, K R Khusnutdinova, “The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type”, J Phys A Math Gen, 37:8 (2004), 2949
I. A. Taimanov, “Dirac Operators and Conformal Invariants of Tori in 3-Space”, Proc. Steklov Inst. Math., 244 (2004), 233–263
O. M. Kiselev, “Asymptotics of solutions of higher-dimensional integrable equations and their perturbations”, Journal of Mathematical Sciences, 138:6 (2006), 6067–6230
I. Krichever, M. Mineev-Weinstein, P. Wiegmann, A. Zabrodin, “Laplacian growth and Whitham equations of soliton theory”, Physica D: Nonlinear Phenomena, 198:1-2 (2004), 1
E.V. Ferapontov, K.R. Khusnutdinova, “On the Integrability of (2+1)-Dimensional Quasilinear Systems”, Commun. Math. Phys, 248:1 (2004), 187
A Ya Maltsev, “Weakly nonlocal symplectic structures, Whitham method and weakly nonlocal symplectic structures of hydrodynamic type”, J Phys A Math Gen, 38:3 (2005), 637
A. V. Zabrodin, “Whitham hierarchy in growth problems”, Theoret. and Math. Phys., 142:2 (2005), 166–182
Mikhail Kovalyov, Ion Bica, “Some properties of slowly decaying oscillatory solutions of KP”, Chaos, Solitons & Fractals, 25:5 (2005), 979
Maxim V. Pavlov, “The Kupershmidt hydrodynamic chains and lattices”, Internat Math Res Notices, 2006 (2006), 1
M. V. Pavlov, “Transformations of integrable hydrodynamic chains and their hydrodynamic reductions”, J. Math. Sci., 151:4 (2008), 3185–3191
I. A. Taimanov, “Two-dimensional Dirac operator and the theory of surfaces”, Russian Math. Surveys, 61:1 (2006), 79–159
Masayuki Oikawa, Hidekazu Tsuji, “Oblique interactions of weakly nonlinear long waves in dispersive systems”, Fluid Dyn Res, 38:12 (2006), 868
Krichever, I, “A characterization of Prym varieties”, International Mathematics Research Notices, 2006, 81476
Grinevich, PG, “Infinitesimal Darboux Transformations of the Spectral Curves of Tori in the Four-Space”, International Mathematics Research Notices, 2007, 005
A. Durán, “Time behaviour of the error when simulating finite-band periodic waves. The case of the KdV equation”, Journal of Computational Physics, 227:3 (2008), 2130
Christoph Bohle, Franz Pedit, Ulrich Pinkall, “The spectral curve of a quaternionic holomorphic line bundle over a 2-torus”, manuscripta math, 2009
Bohle, C, “Discrete holomorphic geometry I. Darboux transformations and spectral curves”, Journal fur Die Reine und Angewandte Mathematik, 637 (2009), 99
G. A. El, A. M. Kamchatnov, M. V. Pavlov, S. A. Zykov, “Kinetic Equation for a Soliton Gas and Its Hydrodynamic Reductions”, J Nonlinear Sci, 2010
Bernard Deconinck, David Lovit, “Data analysis and reduction using stationary solutions of the NLS equation”, Gapa, 89:4 (2010), 611
GUSTAVO DE OLIVEIRA, “ASYMPTOTICS FOR Fermi CURVES: SMALL MAGNETIC POTENTIAL”, Rev. Math. Phys, 22:08 (2010), 881
I. A. Taimanov, “Singular spectral curves in finite-gap integration”, Russian Math. Surveys, 66:1 (2011), 107–144
Grinevich P.G., Novikov S.P., “Singular solitons and indefinite metrics”, Doklady Mathematics, 83:1 (2011), 56–58
Christoph Bohle, Katrin Leschke, Franz Pedit, Ulrich Pinkall, “Conformal maps from a 2-torus to the 4-sphere”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2011, -
Grinevich P.G., Novikov S.P., “Singulyarnye solitony i indefinitnye metriki”, Doklady Akademii nauk, 436:3 (2011), 302–305
Kanehisa Takasaki, Takashi Takebe, “An
$${\hbar}$$
-expansion of the Toda hierarchy”, Anal.Math.Phys, 2012
A. A. Chesnokov, M. V. Pavlov, “Reductions of Kinetic Equations to Finite Component Systems”, Acta Appl Math, 2012
С. Bohle, I. A. Taimanov, “Spectral Curves for Cauchy–Riemann Operators on Punctured Elliptic Curves”, Funct. Anal. Appl., 47:4 (2013), 319–322
Grinevich P.G. Novikov S.P., “Singular Soliton Operators and Indefinite Metrics”, Bull. Braz. Math. Soc., 44:4 (2013), 809–840
B. T. Saparbaeva, “Two-Dimensional Finite-Gap Schrödinger Operators with Elliptic Coefficients”, Math. Notes, 747–749
David Iron, John Rumsey, M.J.. Ward, Juncheng Wei, “Logarithmic Expansions and the Stability of Periodic Patterns of Localized Spots for Reaction–Diffusion Systems in
$${\mathbb {R}}^2$$
R 2”, J Nonlinear Sci, 2014
P. G. Grinevich, A. E. Mironov, S. P. Novikov, “On the non-relativistic two-dimensional purely magnetic supersymmetric Pauli operator”, Russian Math. Surveys, 70:2 (2015), 299–329
T. Claeys, T. Grava, K. D. T.-R. McLaughlin, “Asymptotics for the Partition Function in Two-Cut Random Matrix Models”, Commun. Math. Phys, 2015
P. G. Grinevich, S. P. Novikov, “Singular solitons and spectral meromorphy”, Russian Math. Surveys, 72:6 (2017), 1083–1107
Z. V. Makridin, “An effective algorithm for finding multidimensional conservation laws for integrable systems of hydrodynamic type”, Theoret. and Math. Phys., 194:2 (2018), 274–283
P. G. Grinevich, P. M. Santini, “Phase resonances of the NLS rogue wave recurrence in the quasisymmetric case”, Theoret. and Math. Phys., 196:3 (2018), 1294–1306
A. V. Ilina, I. M. Krichever, N. A. Nekrasov, “Dvumernye periodicheskie operatory Shredingera, integriruemye na «sobstvennom» urovne energii”, Funkts. analiz i ego pril., 53:1 (2019), 31–48
P. G. Grinevich, P. M. Santini, “Konechnozonnyi podkhod v periodicheskoi zadache Koshi dlya anomalnykh voln v nelineinom uravnenii Shredingera pri nalichii neskolkikh neustoichivykh mod”, UMN, 74:2(446) (2019), 27–80
Abenda S. Grinevich P.G., “Reducible M-Curves For Le-Networks in the Totally-Nonnegative Grassmannian and Kp-II Multiline Solitons”, Sel. Math.-New Ser., 25:3 (2019), UNSP 43

Number of views:
This page:	921
Full text:	296
References:	58
First page:	4

What is a QR-code?

Registration

Logotypes