A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of -pseudodifferential operators, valid on an arbitrary regular time scale, is introduced. The linear Poisson tensors and the related Hamiltonians are derived. The quadratic Poisson tensors are given by the use of the recursion operators of the Lax hierarchies. The theory is illustrated by -differential counterparts of Ablowitz–Kaup–Newell–Segur and Kaup–Broer hierarchies.
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Research Article| July 02 2009
Bi-Hamiltonian structures for integrable systems on regular time scales
Błażej M. Szablikowski;
Błażej M. Szablikowski, Maciej Błaszak, Burcu Silindir; Bi-Hamiltonian structures for integrable systems on regular time scales. J. Math. Phys. 1 July 2009; 50 (7): 073502. https://doi.org/10.1063/1.3158860
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