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A Hamiltonian structure associated with a matrix spectral problem of arbitrary-order. (English) Zbl 1209.37070
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:
37K05Hamiltonian structures, symmetries, variational principles, conservation laws
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
37K15Integration of completely integrable systems by inverse spectral and scattering methods