On Hamiltonian perturbations of hyperbolic systems of conservation laws

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.

arXiv comment53 pages

References in corpus (8)

• An integrable shallow water equation with peaked solitons
• Deformations of Semisimple Bihamiltonian Structures of Hydrodynamic Type
• Compatible Poisson brackets of hydrodynamic type
• Hamiltonian operators and l*-coverings
• Deformations of bihamiltonian structures of hydrodynamic type
• Deformations of the Monge/Riemann hierarchy and approximately integrable systems
• The conservation of the Hamiltonian structures in Whitham's method of averaging
• Hyperbolic systems of conservation laws in one space dimension

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