00701nas a2200121   4500008004300000245009900043210006900142520027900211100002000490700001500510700001800525856003600543       2008                        en_Ud  00aFrobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures0 aFrobenius Manifolds and Central Invariants for the Drinfeld Soko3 aThe 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.1 aDubrovin, Boris1 aSi-Qi, Liu1 aYoujin, Zhang  uhttp://hdl.handle.net/1963/252301265nas a2200121   4500008004300000245012600043210006900169520081600238100002001054700001501074700001801089856003601107       2006                        en_Ud  00aOn Hamiltonian perturbations of hyperbolic systems of conservation laws I: quasitriviality of bihamiltonian perturbations0 aHamiltonian perturbations of hyperbolic systems of conservation 3 aWe 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.1 aDubrovin, Boris1 aSi-Qi, Liu1 aYoujin, Zhang  uhttp://hdl.handle.net/1963/2535