Casoratian formulae and solutions to some ABS lattice equations

Da-Jun Zhang (Shanghai University)

Wednesday 17th June, 2009 15:00-16:00 Mathematics Building, room 204


The ABS list consists of nine integrable lattice equations which are classified by Alder, Bobenko and Suris according to the ‘Consistency-around-the cube’ (CAC) and some mild additional assumption. We will talk about find solutions to to some ABS lattice equations. The talk consists of two parts. The Part I focus on a constructive approach for solutions which is based on Darboux transformation from CAC, and then bilinearizations of some ABS lattice equations. In part II we will see derivations of Casoratian formulae and proofs of solutions in Casoratian form.

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