## References

SHOWING 1-10 OF 24 REFERENCES

### Differential-geometric Poisson brackets on a lattice

- Mathematics
- 1989

The concept of differential-geometric Poisson brackets (DGPB) was introduced in [i] in connection with an investigation of the properties of Poisson brackets of hydrodynamic type [2] and their…

### Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants

- Mathematics
- 2001

We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov - Witten invariants of all genera into the…

### The Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogoliubov-Whitham averaging method

- Mathematics
- 1983

Theorem 1. 1) Under local changes of the fields u = u(w) the coefficient g(u) in the bracket (2) transforms like a bilinear form (a tensor with upper indices); if det g 6= 0, then the expression b k…

### ON POISSON BRACKETS OF HYDRODYNAMIC TYPE

- Mathematics
- 2008

I. Riemannian geometry of multidimensional Poisson brackets of hydrodynamic type. In [1] we developed the Hamiltonian formalism of general onedimensional systems of hydrodynamic type. Now suppose…

### Lie bialgebras, Poisson Lie groups and dressing transformations

- Mathematics
- 1997

In this course, we present an elementary introduction, including the proofs of the main theorems, to the theory of Lie bialgebras and Poisson Lie groups and its applications to the theory of…

### Integrable Dynamical Systems Associated with the KdV Equation

- Mathematics, Physics
- 1988

An isospectral deformation representation is constructed for a countable set of dynamical systems with a quadratic nonlinearity, which become the Korteweg-de Vries equation in the continuum limit.…

### SOME CONSTRUCTIONS OF INTEGRABLE DYNAMICAL SYSTEMS

- Mathematics
- 1988

New constructions of integrable dynamical systems are found that admit representation as Lax matrix equations. A countable set of integrable systems is constructed which in the continuous limit turn…

### Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems

- Mathematics
- 1998

ContentsIntroduction Chapter I. Differential geometry of symplectic structures on loop spaces of smooth manifolds § 1.1. Symplectic and Poisson structures on loop spaces of smooth manifolds. Basic…

### Hamiltonian methods in the theory of solitons

- Mathematics
- 1987

The Nonlinear Schrodinger Equation (NS Model).- Zero Curvature Representation.- The Riemann Problem.- The Hamiltonian Formulation.- General Theory of Integrable Evolution Equations.- Basic Examples…

### The Hamiltonian Structure of the Bogoyavlensky Lattice

- Mathematics, Physics
- 1999

We study the Hamiltonian structure of the Bogoyavlensky lattice, which is an integrable differential-difference equation and is a generalization of the Volterra model. We construct the lattice W…