%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