TY - JOUR
T1 - Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures
JF - Adv. Math. 219 (2008) 780-837
Y1 - 2008
A1 - Boris Dubrovin
A1 - Liu Si-Qi
A1 - Zhang Youjin
AB - The Drinfeld - Sokolov construction associates a hierarchy of bihamiltonian integrable systems with every untwisted affine Lie algebra. We compute the complete set of invariants of the related bihamiltonian structures with respect to the group of Miura type transformations.
UR - http://hdl.handle.net/1963/2523
U1 - 1595
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - On Hamiltonian perturbations of hyperbolic systems of conservation laws I: quasitriviality of bihamiltonian perturbations
JF - Comm. Pure Appl. Math. 59 (2006) 559-615
Y1 - 2006
A1 - Boris Dubrovin
A1 - Liu Si-Qi
A1 - Zhang Youjin
AB - We study the general structure of formal perturbative solutions to the Hamiltonian perturbations of spatially one-dimensional systems of hyperbolic PDEs. Under certain genericity assumptions it is proved that any bihamiltonian perturbation can be eliminated in all orders of the perturbative expansion by a change of coordinates on the infinite jet space depending rationally on the derivatives. The main tools is in constructing of the so-called quasi-Miura transformation of jet coordinates eliminating an arbitrary deformation of a semisimple bihamiltonian structure of hydrodynamic type (the quasitriviality theorem). We also describe, following \\\\cite{LZ1}, the invariants of such bihamiltonian structures with respect to the group of Miura-type transformations depending polynomially on the derivatives.
UR - http://hdl.handle.net/1963/2535
U1 - 1583
U2 - Mathematics
U3 - Mathematical Physics
ER -