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Zbl 1238.37020
Ma, Wen-Xiu
Variational identities and applications to Hamiltonian structures of soliton equations. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e-Suppl., e1716-e1726 (2009). ISSN 0362-546X

Summary: This is an introductory report concerning our recent research on Hamiltonian structures. We will discuss variational identities associated with continuous and discrete spectral problems, and their applications to Hamiltonian structures of soliton equations. Our illustrative examples are the AKNS hierarchy and the Volterra lattice hierarchy associated with semisimple Lie algebras, and two hierarchies of their integrable couplings associated with non-semisimple Lie algebras. The resulting Hamiltonian structures generate infinitely many commuting symmetries and conservation laws for the four soliton hierarchies. The presented variational identities can be applied to Hamiltonian structures of other soliton hierarchies.

MSC 2000:: *37K05 Hamiltonian structures, etc.
37K10 Completely integrable systems etc.
35Q51 Solitons

Keywords: variational identities; Hamiltonian structures; zero curvature equations

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