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- O I Mokhov, E V Ferapontov
- 1996

Let us consider a function of n independent variables F (t n) satisfying the following two conditions: 1. The matrix η αβ = ∂ 3 F ∂t 1 ∂t α ∂t β is constant and nondegenerate. Note that the matrix η αβ completely determines dependence of the function F on the fixed variable t 1 .

- OLEG I. MOKHOV
- 2002

We solve the problem of description of nonsingular pairs of compatible flat metrics for the general N-component case. The integrable nonlinear partial differential equations describing all nonsingular pairs of compatible flat metrics (or, in other words, nonsingular flat pencils of metrics) are found and integrated. The integrating of these equations is… (More)

- Oleg Mokhov
- 1995

We consider some differential geometric classes of local and nonlocal Poisson and symplectic structures on loop spaces of smooth manifolds which give natural Hamiltonian or multihamiltonian representations for some important nonlinear equations of mathematical physics and field theory such as nonlinear sigma models with torsion, degenerate Lagrangian… (More)

- O. I. Mokhov
- 2002

In the present work, the integrable bi-Hamiltonian hierarchies related to compatible nonlocal Poisson brackets of hydrodynamic type are effectively constructed. For achieving this aim, first of all, the problem on the canonical form of a special type for compatible nonlocal Poisson brackets of hydrodynamic type is solved. The compatible pairs of nonlocal… (More)

- O. I. Mokhov
- 2008

1 (Dubrovin–Novikov Hamiltonian operator [1]) is compatible with a nondegenerate local Hamiltonian operator of hydrodynamic type K 2 if and only if the operator K 1 is locally the Lie derivative of the operator K 2 along a vector field in the corresponding domain of local coordinates. This result gives, first of all, a convenient general invariant criterion… (More)

- O. I. Mokhov
- 2000

In this paper, notions of compatible and almost compatible Riemannian and pseudo-Riemannian metrics, which are motivated by the theory of compatible (local and nonlocal) Poisson structures of hydrodynamic type and generalize the notion of flat pencil of metrics (this notion plays an important role in the theory of integrable systems of hydrodynamic type and… (More)

- O. I. Mokhov
- 2004

In this paper we solve the problem of describing all nonlocal Hamiltonian operators of hydrodynamic type with flat metrics and establish that this nontrivial special class of Hamiltonian operators is closely connected with the associativity equations of twodimensional topological quantum field theories and the theory of Frobenius manifolds. It is shown that… (More)

- Oleg I. Mokhov
- ArXiv
- 2008

Consider the square lattice Z with vertices at points with integer-valued coordinates in R = {(x1, x2)| xk ∈ R, k = 1, 2} and complex (or real) scalar fields u on the lattice Z, u : Z → C, that are defined by their values ui1i2 , ui1i2 ∈ C, at each vertex of the lattice with the coordinates (i1, i2), ik ∈ Z, k = 1, 2. Consider a class of two-dimensional… (More)

- Oleg I. Mokhov
- ArXiv
- 2009

We consider a special class of two-dimensional discrete equations defined by relations on elementary N ×N squares, N > 2, of the square lattice Z, and propose a new type of consistency conditions on cubic lattices for such discrete equations that is connected to bending elementary N × N squares, N > 2, in the cubic lattice Z. For an arbitrary N we prove… (More)

- O. I. Mokhov
- 2008

We introduce a very natural class of potential submanifolds in pseudo-Euclidean spaces (each Ndimensional potential submanifold is a special flat torsionless submanifold in a 2N-dimensional pseudoEuclidean space) and prove that each N-dimensional Frobenius manifold can be locally represented as an N-dimensional potential submanifold. We show that all… (More)