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

References in corpus (1)

• On Hamiltonian perturbations of hyperbolic systems of conservation laws

Cited by in corpus (1)

• Jacobi Structures of Evolutionary Partial Differential Equations