On Hamiltonian perturbations of hyperbolic systems of conservation laws
Boris Dubrovin, Si-Qi Liu, Youjin Zhang
Abstract
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 LZ1, the invariants of such bihamiltonian structures with respect to the group of Miura-type transformations depending polynomially on the derivatives.
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