Geometry of Differential Forms (Translations of Mathematical Monographs, Vol. 201)

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All-Union Conf. Petrovskii on his seventy-fifth birthday, Moscow State University , M. Algebraic geometry and mathematical physics, Proc. Modern geometry. Methods and applications, Nauka, Moscow , with B. Dubrovin and A. Holomorphic fiberings and non-linear equations. Finite zone solutions of rank 2, Dokl. Solutions to the Ginzburg-Landau equations for planar textures in superfluid He-3, Comm.

Golo and M. Methods of qualitative theory of dynamics systems in general relativity theory, Non-linear waves, Nauka, Moscow , , with O. Holomorphic bundles over algebraic curves and nonlinear equations. The theory of solitons and method of the inverse problem, Nauka, Moscow , with V. Zakharov, S. Manakov, and L.

P Pitaevskii. Ground states of a two-dimensional electron in a periodic magnetic field. Ground states in a periodic field. Magnetic Bloch functions and vector bundles. A method of solving the periodic problem for the KdV equations and its generalization, in Solitons, ed R. Bullough and P. Linear operators and integrable Hamiltonian systems, Proc. Helsinki , Helsinki, Multivalued functions and functionals. An analogue of the Morse theory, Dokl. Periodic solutions of the Kirchhoff equations for the free motion of a rigid body in a fluid and the extended Lyusternik-Shnirel'man-Morse theory.

Variational methods and periodic solutions of equations of Kirchhoff type. II, Funktsional Anal. Bloch functions in a magnetic field and vector bundles. Typical dispersion relations and their quantum numbers, Dokl. Kirchhoff type equations and many-valued functions and functionals.

Analogue of the Morse-Lyusternik-Shnirel'man theory and periodic orbits in a magnetic field, Report to the I. Petrovskii seminar, Uspekhi Mat. Algebraic geometry and mathematical physics, in Proc. Zakharov and S. Manakov, North-Holland, Amsterdam with I. The Hamiltonian formalism and a many-valued analogue of Morse theory, Uspekhi Mat. Nauk , , v. On Poisson brackets compatible with algebraic geometry and the Korteweg-de Vries dynamics on the set of finite-zone potentials, Dokl.

Algebro-geometric Poisson brackets for real finite-zone solutions of the sine-Gordon equation and the non-linear Schroedinger equations, Dokl. On the spectral theory of commuting operators of rank 2 with periodic coefficients , Funktsional Anal. Topological and algebraic-geometrical methods in contemporary mathematical physics, Soviet Scientific Reviews, , v.

Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogolyubov-Whitham averaging method, Dokl. Two-dimensional Schroedinger operators in periodic fields. Multivalued functionals in modern mathematical physics, Atti Accad. Torino Cl. Natur, , v. The analytic generalized Hopf invariant.

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Geometry & Topology Monographs, Volume 13 ()

Many-valued functionals, Uspekhi Mat. Critical points and level surfaces of many-valued functions, Trudy Mat. Steklov, , v. Poisson brackets and complex tori. Trudy Mat. Methods of homology theory, Nauka, Moscow with B. Periodic extremals of many-valued or not everywhere positive functionals, Dokl. On Poisson brackets of hydrodynamic type, Dokl.

Discussion with Academician S. Novikov, Kvant, , N 10, Finite-zone two-dimensional potential Schroedinger operators. Explicit formulas and evolution equations, Dokl. Finite-zone two-dimensional Schroedinger operators. Potential operators, Dokl. Algebro-topological approach to reality problems Real action variables in the theory of finite-gap solutions of the sine-Gordon equation. LOMI, , v.

The geometry of conservative systems of hydrodynamic type. The method of averaging for field-theoretical systems. Poisson brackets of hydrodynamic type, Frobenius algebras and Lie algebras, Dokl. Analytical homotopy theory. Rigidity of homotopic integrals, Dokl. Integrable systems, I. Current problem in mathematics. Fundamental directions. Two-dimensional periodic Schroedinger operators and Prym's q -functions , in Geometry Today, Internat.

Rome, June , Boston , , with A. Veselov and I. Differential geometry and the averaging method for field-theoretic systems, Proc. III Internat. Institute of Nuclear Research, Dubna, , vol. Methods and applications. Bloch homology. Critical points of functions and closed I-forms , Dokl. Morse inequalities and von Neumann 1-factors , Dokl. Topology I. Two-dimensional Schroedinger operators: Inverse scattering transform and evolutional equations, Phys. D18, , with A.

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Vladimir Abramovich Rokhlin obituary , Uspekhi Mat. Arnol'd, D. Fuks, A. Kolmogorov, Ya. Sinai, A. Vershik, and O. Evolution of the Whitham zone in the Korteweg-de Vries theory , Dokl. Elements of differential geometry and topology, Nauk, Moscow , with A. Avilov and I. Algebras of Virasoro type, Riemann surfaces and structures of the theory of solitons , Funktsional. Virasoro-type algebras, Riemann surfaces and strings in Minkowski space , Funktsional.

Two-dimensional Schroedinger operator and solitons: 3-dimensional integrable systems. VIII Internat. Physics, Marseille , World Scientific Publ. The two-dimensional inverse scattering problem for negative energy and generalized analytic functions , I. Energy below the basis state, Funktsional. Algebras of Virasoro type, energy-momentum tensor and decomposition operators on Riemann surfaces , Funktsional. Hydrodynamics of the soliton lattices. Differential geometry and Hamiltonian formalism. Riemann surfaces, operator fields, strings. Brink, D.

Friedan, A. Polyakov, World Scientific, Singapore , , with I. On the quantization of finite-zoned potentials in connection with string theory , Funktsional. Riemann Surfaces, Operator Fields, Strings. Analogues of the Fourrier-Laurent bases. Hydrodynamics of the Soliton Lattices and Differential Geometry. Collection of the survey articles. Various doubles of the Hopf algebras. Operator algebras on the quantum groups and Complex Cobordisms, Uspekhi Math.

Mauk, , v. Integrability in Mathematics and Theoretical Physics: Solitons. The Mathematical Intelligencer, , Vol. Springer-Verlag , New York. Role of Integrable Models in the development of Mathematics. Mathematical Research today and tomorrow: Viewpoints of seven Fields Medallists. LNM, , v , Springer Houston , TX Publish or Perish, , Uspechi Math. Nauk - Russian Math Surveys, , v. Hydrodynamics of Soliton Lattices. Mathematical Physics Reviews, ed by B. Dubrovin and S.

String Equation - 2. Physical Solution, Algebra and Analysis, , v. Solitons and Geometry. Fermi lectures Scuola Norm. Press, Nonselfinersecting magnetic orbits on the plane. Exactly solvable periodic 2-d Schroedinger operators. Russian Math. Surveys, , v 50, n. Encyclopedia of Mathematical Sciences, Springer Verlag, , vol. Topological quantum characteristics observed in the investigation of conductivity in normal metals , JETP Letters, vol. Algebraic properties of 2D difference operators. Russia Math Surveys, , vol 52, iss 1, pp Surveys, , vol 52, iss 5, pp Dynnikov Laplace Transformations and Simplicial Connections.

Schroedinger Operators on Graphs and Topology. Buchstaber and S. Novikov, with A. Veselov Appendix I S. Novikov : Difference Analogs of the Laplace Transformations. Appendix II S. Novikov, A. Taimanov : Difference analogs of the harmonic oscillator. Atiyah and D. World Scientific, Singapore Univ. Press, pp. Discrete Lagrangian Systems on Graphs. Symplecto-Topological Properties. Discrete Schrodinger Operator.


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Published in the volume "Trudy Steklov Math. Pontryagin The levels of quasiperiodic functions on the plane and Hamiltonian systems. Trivalent graphs and solitons. Periodic and almost periodic potentials in inverse problems. Inverse problems, , v. IOP Publishing Ltd. Holomorphic bundles and scalar difference operators. One-point constructions. Holomorphic bundles and commuting difference operators. Two-point constructions. The algebraic aspects of the multiplications in the Complex Cobordisms. Botvinnik, V. Buchstaber, S. Classical and Modern Topology.

Topological Phenomena in Real World Physics. Maltsev ; Real finite-gap solutions to the Sine-Gordon equation; formula for the topological charge. Topological Charge of the real finite-gap periodic Sine-Gordon solutions. Communications on Pure and Applied Mathematics, , v.

On the exotic de-Rham cohomology. Original Title. Friend Reviews.

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