-
Central extensions of Lie algebras, dynamical systems, and symplectic nilmanifolds.
Proc. Steklov Inst. Math. 327 (2024).
-
Finite-zone PT-potentials.
Functional Anal. Appl. 58:4 (2024)
-
On the formality of nearly Kahler manifolds and of Joyce's examples in G_2 holonomy.
Moscow Math. J. 24:4 (2024), 495-512.
(with M. Amann)
-
Floquet-Bloch functions on non-simply-connected manifolds, the Aharonov-Bohm fluxes, and conformal invariants of immersed surfaces.
Proc. Steklov Inst. Math. 325 (2024), 280-291.
-
On unitarity of the scattering operator in non-Hermitian quantum mechanics.
Ann. Henri Poincare 25 (2024), 3899-3909.
(with R.G. Novikov)
-
Geometry and quasiclassical quantization of magnetic monopoles.
Theoret. and Math. Phys 218:1 (2024), 129-144.
-
On a formation of singularities of solutions to soliton equations represented by L,A,B-triples.
Acta Math. Sinica 40:1 (2024), 406-416.
-
Surfaces via spinors and soliton equations.
Proc. Int. Cong. Math. 2022, Vol.4, 2638-2654, EMS Press, Berlin, 2023.
-
Quasi-classical approximation of monopole harmonics.
Math. Notes 114:6 (2023), 1277-1288.
(with Yu.A. Kordyukov)
-
Orthogonal curvilinear coordinate systems and torsion-free sheaves over reducible spectral curves.
Math. Notes 114:4 (2023), 573-582.
(with A.E. Mironov and A. Senninger)
-
On the formality problem for manifolds with special holonomy.
Filomat 37:25 (2023), 8709-8718.
[journal]
-
Rectangular knot diagrams classification with deep learning.
J. Knot Theory and its Ramifications 31:11 (2022), 2250067.
(with L.H. Kauffman and N.E. Russkikh)
[journal]
-
Trace formula for the magnetic Laplacian on a compact hyperbolic surface.
Regular and Chaotic Dynamics 27:4 (2022), 460-476.
(with Yu.A. Kordyukov)
[journal]
-
The second closed geodesic, the fundamental group, and generic Finsler metrińs.
Math. Zeit. 302 (2022), 629-640.
(with H.-B. Rademacher)
[journal]
-
Closed geodesics on connected sums and 3-manifolds.
J. Diff. Geometry 120:3 (2022), 557-573.
(with H.-B. Rademacher)
[journal]
-
Representative elementary volume via averaged scalar Minkowski functionals.
Advanced Problem in Mechanics II, APM 2020, 533-539, Lecture Notes in Mechanical Engineering, Springer, Cham, 2022.
(with M.V. Andreeva, A.V. Kalyuzhnyuk, V.V. Krutko, and N.E. Russkikh)
[book]
-
The Moutard transformation for the Davey-Stewartson II equation and its geometrical meaning.
Math. Notes 110:5 (2021), 754-766.
[journal]
-
Quasi-classical approximation for magnetic monopoles.
Russian Math. Surveys 75:6 (2020), 1067-1088.
(with Yu.A. Kordyukov)
[journal]
-
Trace formula for the magnetic Laplacian.
Russian Math. Surveys 74:2 (2019), 325-361.
(with Yu.A. Kordyukov)
[journal]
-
Discrete analog of the Jacobi set for vector fields.
Computational Topology in Image Context, 1-11, Lecture Notes in Comput. Sci., 11382, Springer, Cham, 2019.
(with A.N. Adilkhanov and A.V. Pavlov)
[book]
-
Darboux-Moutard transformations and Poincare-Steklov operators.
Proc. Steklov Inst. Math. 302 (2018), 315-324.
(with R.G. Novikov)
[journal]
-
The generalized Kummer construction and cohomology rings of G_2-manifolds.
Sb. Math. 209:12 (2018), 1803-1811.
[journal]
-
Topological characteristics of digital models of geological core.
Machine Learning and Knowledge Extraction, 273-281, Lecture Notes in Comput. Sci., 11015, Springer, Cham, 2018.
(with R.R. Gilmanov, A.V. Kalyuzhnyuk, and A.A. Yakovlev)
[book]
-
A canonical basis of two-cycles on a K3 surface.
Sb. Math. 209:8 (2018), 1248-1256.
[journal]
-
Topological characteristics of oil and gas reservoirs and their applications.
Towards Integrative Machine Learning and Knowledge Extraction, 182-193, Lecture Notes in Comput. Sci., 10344, Lecture Notes in Artificial Intelligence, Springer, Cham, 2017.
(with V.A. Baikov, R.R. Gilmanov, and A.A. Yakovlev)
[book]
-
The multiplicity problem for periodic orbits of magnetic flows on the 2-sphere.
Advanced Nonlinear Studies 17 (2017), 17-30.
(with A. Abbondandolo, L. Asselle, G. Benedetti, and M. Mazzucchelli)
[journal]
-
On numerical study of the discrete spectrum of a two-dimensional Schrodinger operator with soliton potential.
Communications in Nonlinear Science and Numerical Simulation 42 (2017), 83-92.
(with A.N. Adilkhanov)
[journal]
-
On first integrals of geodesic flows on a two-torus.
Proc. Steklov Inst. Math. 295 (2016), 225-242.
[journal]
-
The Moutard transformation of two-dimensional Dirac operators and the conformal geometry of surfaces in four-space.
Math. Notes 100:6 (2016), 835-846.
(with R.M. Matuev)
[journal]
-
Moutard-type transform for matrix generalized analytic functions and gauge transforms.
Russian Math. Surveys 71:5 (2016), 970-972.
(with R.G. Novikov)
[journal]
-
The spaces of non-contractible closed curves in compact space forms.
Sb. Math. 207:10 (2016), 1458-1470.
[journal]
-
On an integrable magnetic geodesic flow on the two-torus.
Regular and Chaotic Dynamics 20 (2015), 667-678.
[journal]
-
On a higher dimensional generalization of Seifert fibrations.
Proc. Steklov Inst. Math. 288 (2015), 145-152.
[journal]
-
Blowing up solutions of the modified Novikov-Veselov equation and minimal surfaces.
Theoret. and Math. Phys. 182:2 (2015), 173-181.
[journal]
-
A fast decaying solution to the modified Novikov-Veselov equation with a one-point singularity.
Doklady Math. 91 (2015), 145-146.
[journal]
-
The Moutard transformation of two-dimensional Dirac operators and the Mobius geometry.
Math. Notes 97:1 (2015), 124-135.
[journal]
-
Euclidean minimal tori with planar ends and elliptic solitons.
Int. Math. Res. Not. IMRN 2015 (2015), no. 14, 5907-5932.
(with C. Bohle)
[journal]
-
Two-dimensional von Neumann-Wigner potentials with a multiple positive eigenvalue.
Functional Anal. Appl. 48:4 (2014), 295-297.
(with R.G. Novikov and S.P. Tsarev)
[journal]
-
Spectral curves for Cauchy-Riemann operators on punctured elliptic curves.
Functional Anal. Appl. 47:4 (2013), 319-322.
(with C. Bohle)
[journal]
-
The Moutard transformation and two-dimensional multi-point delta-type potentials.
Russian Math. Surveys 68:5 (2013), 957-959.
(with R.G. Novikov)
[journal]
-
Numerical analysis of topological characteristics of three-dimensional geological models of oil and gas fields.
Mathematical Modeling 25:10 (2013), 19-31. (Russian)
(with Ya.V. Bazaikin, V.A. Baikov, and A.A. Yakovlev)
[pdf]
-
Faddeev eigenfunctions for two-dimensional Schrodinger operators via the Moutard transformation.
Theoret. and Math. Phys. 176 (2013), 1176-1183.
(with S.P. Tsarev)
[journal]
-
On a numerical algorithm for computing topological characteristics of three-dimensional bodies.
Zh. Vychisl. Mat. Mat. Fiz. 53:4 (2013), 523-530. (Russian)
(with Ya.V. Bazaikin)
[pdf]
-
About a role of mean curvature in magnetic mirror geometry.
Fusion Science and Technology 59t:1 (2011), 190-192.
(with A.A. Skovoroda)
[journal]
-
Singular spectral curves in finite gap integration.
Russian Math. Surveys 66:1 (2011), 107-144.
[journal]
-
Periodic magnetic geodesics on almost every energy level via variational methods.
Regular and Chaotic Dynamics 15 (2010), 598-605.
[journal]
-
The type numbers of closed geodesics.
Regular and Chaotic Dynamics 15 (2010), 84–100.
[journal]
-
Role of the mean curvature in the geometry of magnetic confinement configurations.
Plasma Physics Reports 36 (2010), 819-823.
(with A.A. Skovoroda)
[journal]
-
The Moutard transformation: an algebraic formalism via pseudodifferential operators and applications.
OCAMI (Osaka City University Advanced Mathematical Institute) Study Series, V. 3, 2010, pp. 169-183.
(with S.P. Tsarev)
[pdf]
-
On the Moutard transformation and its applications to spectral theory and soliton equations.
J. of Math. Sciences 170 (2010), 371-387.
(with S.P. Tsarev)
[journal]
-
Blowing up solutions of the Novikov-Veselov equation.
Doklady Math. 77 (2008), 467-468.
(with S.P. Tsarev)
[journal]
-
Spectral conservation laws for periodic nonlinear equations of the Melnikov type.
Amer. Math. Soc. Transl. Ser. 2, V. 224, 2008, P. 125-138.
(with P.G. Grinevich)
[pdf]
-
Two-dimensional rational solitons and their blow-up via the Moutard transformation.
Theoret. and Math. Phys. 157 (2008), 1525-1541.
(with S.P. Tsarev)
[journal]
-
Surfaces in three-dimensional Lie groups in terms of spinors.
RIMS Kokyuroku 1605 (2008), 133-150.
[pdf]
-
Two-dimensional Schrodinger operators with fast decaying rational potential and multidimensional
L2-kernel.
Russian Math. Surveys 62:3 (2007), 631-633.
(with S.P. Tsarev)
[journal]
- Infinitesimal Darboux transformations of the spectral curves of
tori in the four-space.
International Mathematics Research Notices 2007 (2007), rnm005, 1-21.
(with P.G. Grinevich)
[journal]
-
Surfaces of revolution in the Heisenberg group and
the spectral generalization of the Willmore functional.
Siberian Math. J. 48:3 (2007), 395-407.
(with D.A. Berdinsky)
[journal]
- Some algebraic examples of Frobenius manifolds.
Theoret. and Math. Phys. 151 (2007), 604-613.
(with A.E. Mironov)
[journal]
- Orthogonal curvilinear coordinate systems corresponding to singular spectral curves.
Proc. Steklov Inst. Math. 255 (2006), 169-184.
(with A.E. Mironov)
[journal]
-
Two-dimensional Dirac operator and surface theory.
Russian Math. Surveys 61:1 (2006), 79-159.
[journal]
-
Surfaces in the four-space and the Davey-Stewartson equations.
Journal of Geometry and Physics 56 (2006), 1235-1256.
[journal]
- Surfaces in three-dimensional Lie groups.
Siberian Math. J. 46:6 (2005), 1005-1019.
(with D.A. Berdinsky)
[journal]
- On the integrability of the n-centre problem.
Mathematische Annalen 331 (2005), 631--649.
(with A. Knauf)
[journal]
- Finite gap theory of the Clifford torus.
International Mathematics Research Notices (2005), 103-120.
[journal]
- Geometric properties of dynamical systems.
Proceedings of the conference "Mathematics, Mechanics, and
Informatics - 2002" dedicated to 10th anniversary of RFBR,
Moscow: Fizmatlit, 2005. P. 276-288.
[pdf]
-
The integrability of the n-center problem at high energies.
Doklady Math. 70 (2004), 502-503.
(with A. Knauf)
[pdf]
-
An example of jump from chaos to integrability in magnetic geodesic flows.
Math. Notes 76 (2004), 587-589.
[journal]
-
Tame integrals of motion and o-minimal structures.
Amer. Math. Soc. Transl. Ser. 2, V. 212, 2004, P. 317-324.
[pdf]
-
Dirac operators and conformal invariants of tori in the three-space.
Proc. Steklov Inst. Math. 244 (2004), 233-263.
[pdf]
-
On two-dimensional finite-gap potential Schrodinger and Dirac operators
with singular spectral curves.
Siberian Math. J. 44:4 (2003), 686-694.
[journal]
-
On the formality problem for symplectic manifolds.
AMS. Contemp. Math., V. 288 (2001), 1-9.
(with I.K. Babenko)
[pdf]
-
Integrable geodesic flows on the suspensions of toric automorphisms.
Proc. Steklov Inst. Math. 231 (2000), 42-58.
(with A.V. Bolsinov)
[pdf]
-
Massey products in symplectic manifolds.
Sb. Math. 191 (2000), 1107-1146.
(with I.K. Babenko)
[journal]
-
Integrable geodesic flows with positive topological entropy.
Inventiones Mathematicae 140 (2000), 639-650.
(with A.V. Bolsinov)
[journal]
-
On nonformal simply connected symplectic manifolds.
Siberian Math. J. 41:2 (2000), 204-217.
(with I.K. Babenko)
[journal]
-
An example of an integrable geodesic flow with positive
topological entropy.
Russian Math. Surveys 54:4 (1999), 833-834.
(with A.V. Bolsinov)
[journal]
-
Finite-gap solutions of the modified Novikov-Veselov equation,
their spectral properties, and applications.
Siberian Math. J. 40 (1999), 1146-1156.
[journal]
-
The Weierstrass representation of spheres, the Willmore numbers, and
soliton spheres.
Proc. Steklov Inst. Math. 225 (1999), 222-243.
[pdf]
-
A remark on positively curved manifolds of dimensions 7 and 13.
Tensor and Vector Analysis, Gordon and Breach, Amsterdam, 1998, 282-295.
[pdf]
-
On the existence of nonformal simply connected symplectic manifolds.
Russian Math. Surveys 53:5 (1998), 1082-1083.
(with I.K. Babenko)
[journal]
-
The Weierstrass representation of closed surfaces in
R3.
Functional Anal. Appl. 32:4 (1998), 258-267.
[journal]
-
Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems.
Trans. Amer. Math. Soc. 350 (1998), 2697-2717.
(with A. Bahri)
[journal]
-
Some problems related to topology of manifolds with positive sectional
curvature.
Siberian Adv. Math. 8:4 (1998), 84-108.
[pdf]
-
The global Weierstrass representation and its spectrum.
Russian Math. Surveys 52:6 (1997), 1330-1332.
[journal]
- Surfaces of revolution in terms of solitons.
Ann. Glob. Anal. Geom. 15 (1997), 419-435.
[journal]
-
Secants of abelian varieties, theta functions and soliton equations.
Russian Math. Surveys 52:1 (1997), 147-218.
[journal]
-
Integrable geodesic flows of non-holonomic metrics.
Journal of Dynamical Systems and Control Theory 3 (1997), 129-147.
[journal]
-
Difference analogs of the harmonic oscillator.
Amer. Math. Soc. Transl. Ser. 2, V. 179, 1997, P. 126-130.
(with S.P. Novikov)
[pdf]
-
Modified Novikov-Veselov equation and differential geometry
of surfaces.
Amer. Math. Soc. Transl. Ser. 2, V. 179, 1997, P. 133-151.
[pdf]
-
On totally geodesic embeddings of 7-dimensional manifolds into
13-dimensional manifolds of positive sectional curvature.
Sb. Math. 187 (1996), no. 12, 1853-1867.
[journal]
-
Constant mean curvature surfaces via an integrable dynamical system.
J. Phys. A : Math. Gen. 29 (1996), 1261-1265.
(with B.G. Konopelchenko)
[journal]
- On the two-gap elliptic potentials.
Acta Applicandae Math. 36 (1994), 119-124.
[journal]
-
The topology of Riemannian manifolds with integrable geodesic flows.
Proc. Steklov Inst. Math. 205 (1995), 139-150.
[pdf]
- Closed geodesics on non-simply connected manifolds.
Siberian Math. J. 34 (1993), 1154-1160.
[journal]
-
The Landau-Lifshits equation and quadruple secants of Prym varieties.
Functional Anal. Appl. 27 (1993), 222-224.
[journal]
-
Closed non-self-intersecting extremals of multivalued functionals.
Siberian Math. J. 33 (1992), 686-692.
[journal]
-
On the existence of three nonintersecting closed geodesics on manifolds
that are homeomorphic to the two-dimensional sphere.
Russian Acad. Sci. Izv. Math. 40 (1993), 565-590.
[journal]
-
Closed extremals on two-dimensional manifolds.
Russian Math. Surveys 47:2 (1992), 163-211.
[journal]
-
Non-self-intersecting closed extremals of multivalued or
not-everywhere-positive functionals.
Math. USSR-Izv. 38 (1992), 359-374.
[pdf]
-
Prym theta functions and hierarchies of nonlinear equations.
Math. Notes 50 (1992), 723-730.
[journal]
-
Prym varieties of branched coverings, and nonlinear equations.
Math. USSR-Sb. 70 (1991), 367-384.
[pdf]
-
Two-dimensional finite-zone Schrodinger potential operators.
Functional Anal. Appl. 24 (1990), no. 1, 76-77.
[journal]
-
Elliptic solutions of nonlinear equations.
Theoret. and Math. Phys. 84 (1991), 700-706.
[journal]
-
Multivalued finite-zone solutions of the equation
D u = sin u.
Math. Notes 47 (1990), 293-297.
[journal]
-
Smooth real finite-zone solutions of sine-Gordon type equations.
Math. Notes 47 (1990), 94-100.
[journal]
-
On topological properties of integrable geodesic flows.
Mathematical Notes 44:2 (1988), 283-284. (Russian)
[pdf]
-
Topological obstructions to the integrability of geodesic flows on
nonsimply connected manifolds.
Math. USSR-Izv. 30 (1988), 403-409.
[pdf]
-
On an analogue of the Novikov conjecture in a problem of Riemann-Schottky
type for Prym varieties.
Sov. Math. Dokl. 35 (1987), 420-424.
[pdf]
-
Effectivization of theta-function formulas for two-dimensional
Schrodinger potential operators that are finite-gap at a certain energy
level.
Sov. Math. Dokl. 32 (1985), 843-846.
[pdf]
-
Closed geodesics on non-simply-connected manifolds.
Russian Math. Surveys 40:6 (1986), 143-144.
[pdf]
-
Periodic extremals of multivalued or not everywhere positive functionals.
Sov. Math. Dokl. 29 (1984), 18-20.
(with S.P. Novikov)
[pdf]
-
The principle of throwing out cycles in Morse-Novikov theory.
Sov. Math. Dokl. 27 (1983), 43-46.
[pdf]
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