- Oleksandr Chvartatskyi (Mathematical Institute, University of Göttingen)
Title of talk: Binary Darboux transformations in bidifferential calculus
Abstract: In the framework of bidifferential calculus, we apply a universal binary Darboux transformation result to obtain infinite families of exact solutions of several integrable equations in more than two dimensions. This includes the selfdual Yang-Mills equation, a generalization of Hirota's bilinear difference equation, the matrix (potential) KP, and matrix versions of the Davey-Stewartson and the two-dimensional Toda lattice equations. - Aristophanes Dimakis (University of the Aegean, Chios, Greece)
Title of talk: Simplex and polygon equations
Abstract: In the same way as simplex equations (including the Yang-Baxter equation) are related to (higher) Bruhat orders, there is a family of equations related to (higher) Tamari orders, which are constructed from the (higher) Bruhat orders. These "polygon equations" include the well-known pentagon equation. We also present a geometric interpretation of the structure of these equations as deformations of maximal chains on polyhedra. - Adam Doliwa (University of Warmia and Mazury, Olsztyn, Poland)
Title of talk: Discrete KP Equation with Self-Consistent Sources
Abstract: We show that the discrete Kadomtsev-Petviashvili (KP) equation with sources, obtained recently by the "source generalization" method, can be incorporated into the squared eigenfunctions symmetry extension procedure. Moreover, using the known correspondence between Darboux-type transformations and additional independent variables, we demonstrate that the equation with sources can be derived from Hirota's discrete KP system of equations (without sources) in a space of bigger dimension. In this way we uncover the origin of the source terms as coming from multidimensional consistency of the Hirota system itself. - Ludwig Faddeev (St. Petersburg, Russia, presently Institute for Theoretical Physics, University of Göttingen)
Title of talk: Discrete time evolution for zero modes in quantum Liouville models - Eugene Ferapontov (Loughborough University, UK)
Title of talk: Dispersionless integrable systems in 3D and Einstein-Weyl geometry
Abstract: For several classes of second order dispersionless PDEs, we show that the symbols of their formal linearizations define conformal structures which must be Einstein-Weyl in 3D (or selfdual in 4D) if and only if the PDE is integrable by the method of hydrodynamic reductions. This demonstrates that the integrability of dispersionless PDEs can be seen from the geometry of their formal linearizations. (J. Diff. Geom. (2014); arXiv:1208.2728v1) - Folkert Müller-Hoissen (Max Planck Institute for Dynamics and Self-Organization, Göttingen)
Title of talk: 'Riemann equations' in bidifferential calculus
Abstract: In the algebraic framework of bidifferential calculus, we consider equations that formally resemble a (matrix) Riemann equation (inviscid Burgers equation). Depending on the choice of first-order bidifferential calculus, such equations can be of a rather different nature, however, and several examples will be presented. A recent (also non-isospectral) binary Darboux transformation result in bidifferential calculus can be specialized to generate exact solutions. If the calculus extends to second order, compatible systems of such equations have well-known integrable systems like sdYM, KP, Toda, Hirota-Miwa, DS, as integrability conditions.