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Zbl 1192.37091
Ma, Wen-Xiu; Zhang, Yi
Component-trace identities for Hamiltonian structures. (English)
[J] Appl. Anal. 89, No. 4, 457-472 (2010). ISSN 0003-6811; ISSN 1563-504X/e

Summary: We show that on a particular class of semi-direct sums of matrix Lie algebras, component traces of the matrix product can produce bilinear forms which are non-degenerate, symmetric and invariant under the Lie product. The corresponding variational identities are called component-trace identities and provide tools in generating Hamiltonian structures of integrable couplings including the perturbation equations. An illustrative example of applying component-trace identities is given for the KdV hierarchy.

MSC 2000:: *37K05 Hamiltonian structures, etc.
35Q53 KdV-like equations
37K10 Completely integrable systems etc.
37K30 Relations with algebraic structures

Keywords: Hamiltonian structures; integrable couplings; zero-curvature equations; matrix Lie algebras

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Zentralblatt MATH Berlin [Germany]