01265nas 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