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Zbl 1209.37070
Ma, Wen-Xiu
A Hamiltonian structure associated with a matrix spectral problem of arbitrary-order. (English)
[J] Phys. Lett., A 367, No. 6, 473-477 (2007). ISSN 0375-9601

Summary: Starting from a specific matrix iso-spectral problem, an associated hierarchy of multi-component Hamiltonian equations is constructed, based on zero curvature equations. The key point is to choose appropriate time parts of Lax pairs which can yield evolution equations, and the existence of a Hamiltonian structure for the obtained hierarchy is established by means of the trace identity. An example with five components is computed, along with its Hamiltonian structure.

MSC 2000:: *37K05 Hamiltonian structures, etc.
37K10 Completely integrable systems etc.
37K15 Integration by inverse spectral and scattering methods

Keywords: matrix spectral problem; soliton hierarchy; Hamiltonian structure; trace identity

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