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Letters in Mathematical Physics

, Volume 84, Issue 1, pp 47–63 | Cite as

On Properties of Hamiltonian Structures for a Class of Evolutionary PDEs

  • Si-Qi Liu
  • Chao-Zhong Wu
  • Youjin Zhang
Article

Abstract

In a recent paper we 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.

Mathematics Subject Classification (2000)

Primary: 37K10 Secondary: 35Q53 

Keywords

Hamiltonian structure quasi-Miura transformation quasi-triviality 

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Copyright information

© Springer 2008

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingPeople’s Republic of China

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