%0 Journal Article
%J Adv. Math. 219 (2008) 780-837
%D 2008
%T Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures
%A Boris Dubrovin
%A Liu Si-Qi
%A Zhang Youjin
%X 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.
%B Adv. Math. 219 (2008) 780-837
%G en_US
%U http://hdl.handle.net/1963/2523
%1 1595
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-11T12:52:04Z\\nNo. of bitstreams: 1\\n0710.3115v1.pdf: 569666 bytes, checksum: e3e72944ffd5f097ccaf975d2df90986 (MD5)
%R 10.1016/j.aim.2008.06.009
%0 Journal Article
%J Comm. Pure Appl. Math. 59 (2006) 559-615
%D 2006
%T On Hamiltonian perturbations of hyperbolic systems of conservation laws I: quasitriviality of bihamiltonian perturbations
%A Boris Dubrovin
%A Liu Si-Qi
%A Zhang Youjin
%X 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.
%B Comm. Pure Appl. Math. 59 (2006) 559-615
%G en_US
%U http://hdl.handle.net/1963/2535
%1 1583
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-18T13:01:41Z\\nNo. of bitstreams: 1\\n0410027v2.pdf: 508002 bytes, checksum: 4e8fc8db5fc7512dd54eb832cc52192d (MD5)
%R 10.1002/cpa.20111