An unification of field, lattice and q-deformed soliton systems as integrable evolution equations on regular times scales
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| Description: |
Blazej Szablikowski (Glasgow)
Monday 30 March 2009, 16:15-17:00 Geometric Aspects of Discrete and Ultra-discrete Integrable Systems |
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| Created: | 2011-03-10 13:16 | ||||||||
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| Collection: | Discrete Integrable Systems | ||||||||
| Publisher: | Isaac Newton Institute | ||||||||
| Copyright: | Szablikowski, B | ||||||||
| Language: | eng (English) | ||||||||
| Credits: |
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| Abstract: | A seminar from the Geometric Aspects of Discrete and Ultra-discrete Integrable Systems conference in association with the Newton Institute programme: Discrete Integrable Systems
http://www.gla.ac.uk/departments/mathematics/research/isamp/events/gadudis/programme/ An unified theory of the construction of the bi-Hamiltonian non-linear evolution hierarchies such as field, 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 definition of the trace functional on an algebra of pseudo-differential operators, valid on an arbitrary regular time scale. I will illustrate the theory by differential 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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