Degenerate bi-Hamiltonian Poisson brackets of the hydrodynamic type are studied. They are bi-Hamiltonian structures of certain dispersionless rational Lax equations and are related to the notion of a degenerate Frobenius manifold
We investigate the systems of quasi-linear partial differential equations of hydrody- namic type. Th...
I. Riemannian geometry of multidimensional Poisson brackets of hydro-dynamic type. In [1] we develop...
We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, w...
The bi-Hamiltonian structure of certain multicomponent integrable systems, generalizations of the di...
This paper is concerned with the properties of differential-geometric-type Poisson brackets specifie...
were introduced and studied in [1] and [2] to construct a theory of conservative systems of hydrodyn...
Abstract—A Hamiltonian system on a Poisson manifold M is called integrable if it possesses sufficien...
Systems of quasilinear partial differential equations of the first order, known as hydrodynamic type...
International audienceThe Dubrovin–Zhang hierarchy is a Hamiltonian infinite-dimensional integrable ...
The Poisson brackets of hydrodynamic type, also called Dubrovin-Novikov brackets, constitute the Ham...
Hamiltonian structures for 2- or 3-dimensional incompressible flows with a free boundary are determi...
In our recent paper, we proved the polynomiality of a Poisson bracket for a class of infinite-dimens...
We study the relationship between singularities of bi-Hamiltonian systems and algebraic properties o...
The thesis is organized in three distinct parts. The first part ( § 1 and §2) is purely expository....
We consider the pairs of general weakly nonlocal Poisson brackets of hydrodynamic type (Ferapontov b...
We investigate the systems of quasi-linear partial differential equations of hydrody- namic type. Th...
I. Riemannian geometry of multidimensional Poisson brackets of hydro-dynamic type. In [1] we develop...
We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, w...
The bi-Hamiltonian structure of certain multicomponent integrable systems, generalizations of the di...
This paper is concerned with the properties of differential-geometric-type Poisson brackets specifie...
were introduced and studied in [1] and [2] to construct a theory of conservative systems of hydrodyn...
Abstract—A Hamiltonian system on a Poisson manifold M is called integrable if it possesses sufficien...
Systems of quasilinear partial differential equations of the first order, known as hydrodynamic type...
International audienceThe Dubrovin–Zhang hierarchy is a Hamiltonian infinite-dimensional integrable ...
The Poisson brackets of hydrodynamic type, also called Dubrovin-Novikov brackets, constitute the Ham...
Hamiltonian structures for 2- or 3-dimensional incompressible flows with a free boundary are determi...
In our recent paper, we proved the polynomiality of a Poisson bracket for a class of infinite-dimens...
We study the relationship between singularities of bi-Hamiltonian systems and algebraic properties o...
The thesis is organized in three distinct parts. The first part ( § 1 and §2) is purely expository....
We consider the pairs of general weakly nonlocal Poisson brackets of hydrodynamic type (Ferapontov b...
We investigate the systems of quasi-linear partial differential equations of hydrody- namic type. Th...
I. Riemannian geometry of multidimensional Poisson brackets of hydro-dynamic type. In [1] we develop...
We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, w...
DOI
Add to ORKG