Müller-Hoissen F. Binary Darboux transformations in bidifferential calculus, talk at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic (abstract)

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Speaker: Folkert Müller-Hoissen

Title: Binary Darboux transformations in bidifferential calculus

The algebraic framework of noncommutative geometry allows a wide generalization of gauge theory and, in particular, the zero curvature condition that underlies integrable systems. In particular, this allows to treat integrable differential and difference equations on an equal footing. In the somewhat more specialized setting of bidifferential calculus, we discuss a recent formulation of binary Darboux transformations (A. Dimakis and F. Müller-Hoissen, SIGMA 9 (2013) 009, arXiv:1207.1308) and corresponding applications.