# Müller-Hoissen F. Self-consistent sources for integrable equations via deformations of binary Darboux transformations, talk at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic (abstract)

**Speaker**: Folkert Müller-Hoissen

**Title**: Self-consistent sources for integrable equations via deformations of binary Darboux transformations
**Abstract**:

We reveal the origin and structure of self-consistent source extensions of integrable equations from the perspective of binary Darboux transformations. They arise via a deformation of the potential that is central in this method. As examples, we obtain in particular matrix versions of self-consistent source extensions of the sine-Gordon, nonlinear Schrödinger, KP, Davey-Stewartson, two-dimensional Toda lattice and discrete KP systems. They are accompanied by a hetero binary Darboux transformation that generates solutions of such a system from a solution of the source-free system and solutions of an associated linear system and its adjoint. The essence of all this is encoded in universal equations in the framework of bidifferential calculus. This is joint work with Oleksandr Chvartatskyi and Aristophanes Dimakis.