Integrability and Other Analytical Properties of Nonlinear PDE Systems

Integrability of a nonlinear partial differential equation or a system of such equations, in its basic sense, refers to the possibility of construction of a solution for every initial/boundary value problem within a certain class of problems. However, no common definition of integrability has been recognized to date. In particular, a model that possesses advanced analytical properties may be called integrable (or conjectured to be integrable) in a certain specific sense.