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On Hamiltonian perturbations of hyperbolic systems of conservation laws I: quasitriviality of bihamiltonian perturbations

TitleOn Hamiltonian perturbations of hyperbolic systems of conservation laws I: quasitriviality of bihamiltonian perturbations
Publication TypeJournal Article
Year of Publication2006
AuthorsDubrovin, B, Si-Qi, L, Youjin, Z
JournalComm. Pure Appl. Math. 59 (2006) 559-615
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 \\\\cite{LZ1}, the invariants of such bihamiltonian structures with respect to the group of Miura-type transformations depending polynomially on the derivatives.

URLhttp://hdl.handle.net/1963/2535
DOI10.1002/cpa.20111
Alternate JournalOn Hamiltonian perturbations of hyperbolic systems of conservation laws

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