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- O. I. Mokhov
- 2000

- Oleg Mokhov
- 1995

We consider some differential geometric classes of local and nonlocal Poisson and sym-plectic 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, 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 .

- O. I. Mokhov
- 2008

- O. I. Mokhov
- 2004

Nonlocal Hamiltonian operators of hydrodynamic type with flat metrics, integrable hierarchies and the equations of associativity

- O. I. Mokhov
- 2000

On integrability of the equations for nonsingular pairs of compatible flat metrics

- O. I. Mokhov
- 2002

Compatible nonlocal Poisson brackets of hydrodynamic type, and integrable hierarchies related to them

- O. I. Mokhov
- 2006

We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlin-ear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of potential flat torsionless submanifolds. We show that all potential flat torsionless submanifolds in… (More)

- O. I. Mokhov
- 2002

Compatible metrics of constant Riemannian curvature: local geometry, nonlinear equations and integrability

- O. I. Mokhov
- 2008

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