he proposed mini-symposium aims to bring together experts in Mathematical physics working on problems, related to integrability /exact solvability of nonlinear PDEs. The equations of interest are rich of underlying algebraic and geometric structures which predetermines the variety of mathematical methods used in the area. These methods include spectral theory of operators, functional analysis, geometry, inverse scattering of discrete and continuous integrable systems, symmetry groups and theory of Lie groups and algebras. The focus of the presented results will be on particular solution techniques as well as on qualitative results and further developments of the mathematical methods. An important aim of this mini symposium is also to establish and emphasize the connection of the PDE models under consideration to real life applications in fluid mechanics, nonlinear optics and geophysics.