### 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

Satellite

#### Abstract

An unied 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 denition of the trace functional on an algebra of -pseudo-dierential operators, valid on an arbitrary regular time scale. I will illustrate the theory by -dierential 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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