5 research outputs found
Presymplectic representation of bi-Hamiltonian chain
Liouville integrable systems, which have bi-Hamiltonian representation of the
Gel'fand-Zakharevich type, are considered. Bi-presymplectic representation of
one-Casimir bi-Hamiltonian chains and weakly bi-presymplectic representation of
multi-Casimir bi-Hamiltonian chains are constructed. The reduction procedure
for Poisson and presymplectic structures is presented.Comment: 17 pages, to appear in J. Phys. A: Math. Ge
From dispersionless to soliton systems via Weyl-Moyal like deformations
The formalism of quantization deformation is reviewed and the Weyl-Moyal like
deformation is applied to systematic construction of the field and lattice
integrable soliton systems from Poisson algebras of dispersionless systems.Comment: 26 page
Classical R-matrix theory of dispersionless systems: I. (1+1)-dimension theory
A systematic way of construction of (1+1)-dimensional dispersionless
integrable Hamiltonian systems is presented. The method is based on the
classical R-matrix on Poisson algebras of formal Laurent series. Results are
illustrated with the known and new (1+1)-dimensional dispersionless systems.Comment: 23 page