Introduction:
Essentially, integrability is the field that studies nonlinear equations
for which the dynamics can be determined for long periods of times.
While the property of integrability for differential equations has been
widely studied, the theory of integrable discrete systems is a
relatively new field of research. Just like differential equations
however, finite-difference equations appear in a wide range of
application. The goal of this mini-symposium is to bring together
specialists of this field of research. We will discuss different
existing notions of integrability in the discrete and ultra-discrete
cases and see how these can be used for studying equations arising in
applications. |