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An unification of field, lattice and q-deformed soliton systems as integrable evolution equations on regular times scales

Szablikowski, B (Glasgow)
Monday 30 March 2009, 16:15-17:00



An uni ed theory of the construction of the bi-Hamiltonian nonlinear evolution hierarchies such as eld, lattice and q-discrete soliton hierarchies, will be presented. I will give a brief review of the concept of time scales, including definitions of -derivative and -integral. A construction of the bi-Hamiltonian structures for integrable systems on regular time scales will be presented. The main result consists on the de nition of the trace functional on an algebra of -pseudo-di erential operators, valid on an arbitrary regular time scale. I will illustrate the theory by -di erential counterparts of AKNS and Kaup-Broer hierarchies. The talk will be based on the article: arXiv:0810.0766. (This is joint work with Maciej Blaszak and Burcu Silindir.)


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