Hamiltonian structures and their reciprocal transformations for the r-KdV-CH hierarchy

JOURNAL OF GEOMETRY AND PHYSICS

卷:59

Article

Chen, Ming¹  Liu, Si-Qi¹  Zhang, Youjin¹ 

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

关键词: Hamiltonian structure;    Camassa-Holm hierarchy;    Reciprocal transformations;    Frobenius manifold;    Central invariants;   

DOI  :  10.1016/j.geomphys.2009.06.001

来源: Elsevier

【 摘 要 】

The r-KdV-CH hierarchy is a generalization of the Korteweg-de Vries and Camassa-Holm hierarchies parameterized by r + 1 constants. In this paper we clarify some properties of its multi-Hamiltonian structures including the explicit expressions of the Hamiltonians, the formulae of the central invariants of the associated bihamiltonian structures and the relationship of these bihamiltonian structures with Frobenius manifolds. By introducing a class of generalized Hamiltonian structures, we present in a natural way the transformation formulae of the Hamiltonian structures of the hierarchy under certain reciprocal transformations, and prove the validity of the formulae at the level of dispersionless limit. (c) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free