Dispersive deformations of Hamiltonian systems of hydrodynamic type in 2+1 dimensions

@article{Ferapontov2011DispersiveDO,
  title={Dispersive deformations of Hamiltonian systems of hydrodynamic type in 2+1 dimensions},
  author={Eugene V. Ferapontov and V. S. Novikov and Nikola M. Stoilov},
  journal={Physica D: Nonlinear Phenomena},
  year={2011},
  volume={241},
  pages={2138-2144}
}

Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions and their dispersive deformations

Hamiltonian systems of hydrodynamic type occur in a wide range of applications including fluid dynamics, the Whitham averaging procedure and the theory of Frobenius manifolds. In 1 + 1 dimensions,

On Deformations of Multidimensional Poisson Brackets of Hydrodynamic Type

The theory of Poisson vertex algebras (PVAs) (Barakat et al. in Jpn J Math 4(2):141–252, 2009) is a good framework to treat Hamiltonian partial differential equations. A PVA consists of a pair

On Deformations of Multidimensional Poisson Brackets of Hydrodynamic Type

  • M. Casati
  • Materials Science
    Communications in Mathematical Physics
  • 2014
The theory of Poisson vertex algebras (PVAs) (Barakat et al. in Jpn J Math 4(2):141–252, 2009) is a good framework to treat Hamiltonian partial differential equations. A PVA consists of a pair

References

SHOWING 1-10 OF 28 REFERENCES

Hamiltonian Systems of Hydrodynamic Type in 2 + 1 Dimensions

We investigate multi-dimensional Hamiltonian systems associated with constant Poisson brackets of hydrodynamic type. A complete list of two- and three-component integrable Hamiltonians is obtained.

Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions

Hamiltonian systems of hydrodynamic type occur in a wide range of applications including fluid dynamics, the Whitham averaging procedure, and the theory of Frobenius manifolds. In 1 + 1 dimensions,

Dispersive deformations of hydrodynamic reductions of (2 + 1)D dispersionless integrable systems

We demonstrate that hydrodynamic reductions of dispersionless integrable systems in 2 + 1 dimensions, such as the dispersionless Kadomtsev–Petviashvili (dKP) and dispersionless Toda lattice (dTl)

On Deformation of Poisson Manifolds of Hydrodynamic Type

We study a class of deformations of infinite-dimensional Poisson manifolds of hydrodynamic type which are of interest in the theory of Frobenius manifolds. We prove two results. First, we show that

ON POISSON BRACKETS OF HYDRODYNAMIC TYPE

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

THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD

It is proved that there exists an infinite involutive family of integrals of hydrodynamic type for diagonal Hamiltonian systems of quasilinear equations; the completeness of the family is also

On Hamiltonian Perturbations of Hyperbolic Systems of Conservation Laws, II: Universality of Critical Behaviour

Hamiltonian perturbations of the simplest hyperbolic equation ut + a(u) ux = 0 are studied. We argue that the behaviour of solutions to the perturbed equation near the point of gradient catastrophe

Integrable equations in 2 + 1 dimensions: deformations of dispersionless limits

We classify integrable third-order equations in 2 + 1 dimensions which generalize the examples of Kadomtsev–Petviashvili, Veselov–Novikov and Harry Dym equations. Our approach is based on the

Classical R-matrix theory for bi-Hamiltonian field systems

This is a survey of the application of the classical R-matrix formalism to the construction of infinite-dimensional integrable Hamiltonian field systems. The main point is the study of bi-Hamiltonian

On universality of critical behaviour in Hamiltonian PDEs

Our main goal is the comparative study of singularities of solutions to the systems of first order quasilinear PDEs and their perturbations containing higher derivatives. The study is focused on the