TY - JOUR
T1 - On Hamiltonian perturbations of hyperbolic systems of conservation laws I: quasitriviality of bihamiltonian perturbations
JF - Comm. Pure Appl. Math. 59 (2006) 559-615
Y1 - 2006
A1 - Boris Dubrovin
A1 - Liu Si-Qi
A1 - Zhang Youjin
AB - 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.
UR - http://hdl.handle.net/1963/2535
U1 - 1583
U2 - Mathematics
U3 - Mathematical Physics
ER -