108 citations · 189 across the 17 of their papers we have counts for
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Poisson brackets of hydrodynamic type and their generalizations
A. Ya. Maltsev, S. P. Novikov
In this paper, we consider Hamiltonian structures of hydrodynamic type and some of their generalizations. In particular, we discuss the questions concerning the structure and speci…
Geometry of the triangle equation on two-manifolds
I. A. Dynnikov, S. P. Novikov
A non-traditional approach to the discretization of differential-geometrical connections was suggested by the authors in 1997. At the same time we started studying first order diff…
On the exotic De-Rham cohomology. Perturbation theory as a spectral sequence
S. P. Novikov
This work is dedicated to some new exotic homological constructions associated with the different Morse-type inequalities for differential forms and vector fields. It contains also…
Various doublings of Hopf Algebras. Algebras of Operators on Quantum Groups and Complex Cobordisms
S. P. Novikov
Family of doublings of Hopf algeras based on the product of algebra and its dual are constructed and studied. Special cases of these construction may be considered as natural quant…
The Schrödinger operator on graphs and topology
S. P. Novikov
Symplectic vector-valued scalar product is constructed on the spaces of solutions of the real discrete Shrodinger equation with fixed value of the spectral parameter on graphs. It…
Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds
S. P. Novikov, I. A. Dynnikov
Euler-Darboux-Backlund and Laplace transformations are considered for the one- and two-dimensional Schrodinger operators. Their discrete analogs are constructed and generalized for…
Exactly solvable two-dimensional Schrodinger operators and Laplace transformations
S. P. Novikov, A. P. Veselov
Different cases of sequences of the Laplace Transformations for the 2D Schrodinger operator in the periodic magnetic field and electric potential are considered. They lead to the e…
Periodic and almost periodic potentials in the inverse problems
I. M. Krichever, S. P. Novikov
We review basic ideas and basic examples of the theory of the inverse spectral problems.
The Levels of Quasiperiodic Functions on the plane, Hamiltonian Systems and Topology
S. P. Novikov
Topology of levels of the quasiperiodic functions with m=n+2 periods on the plane is studied. For the case of functions with m=4 periods full description is obtained for the open e…
Discrete Schrodinger operators and topology
S. P. Novikov
This work is a continuation and extension of the note published in the Russian Math Surveys 1997 n 6. For any pair of solutions of the spectral problem for the second order selfadj…