On Properties of Hamiltonian Structures for a Class of Evolutionary PDEs

Abstract

In \cite{LZ2} it is proved that for certain class of perturbations of the hyperbolic equation $u_t=f(u)u_x$, there exist changes of coordinate, called quasi-Miura transformations, that reduce the perturbed equations to the unperturbed one. We prove in the present paper that if in addition the perturbed equations possess Hamiltonian structures of certain type, the same quasi-Miura transformations also reduce the Hamiltonian structures to their leading terms. By applying this result, we obtain a criterion of the existence of Hamiltonian structures for a class of scalar evolutionary PDEs and an algorithm to find out the Hamiltonian structures.

17 pages

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Cited by in corpus (7)

• Bihamiltonian Cohomologies and Integrable Hierarchies I: A Special Case
• On integrable conservation laws
• Jacobi Structures of Evolutionary Partial Differential Equations
• A deformation of the method of characteristics and the Cauchy problem for Hamiltonian PDEs in the small dispersion limit
• Tau Functions and Virasoro Symmetries for Drinfeld-Sokolov Hierarchies
• The Hodge-FVH Correspondence
• Hamiltonian perturbations at the second order approximation