Nonlinear dispersive equations: well-posedness and qualitative properties of solutions

In this talk, we will consider some nonlinear evolution equations of dispersive type. The well-known models that fall in this class of equations are the Korteweg-de Vries (KdV) and the non-linear Schrödinger (NLS) equations. We will discuss some recent techniques to address the well-posedness issues for the initial value problems associated with these models and other systems involving them. Also, we will talk about other qualitative properties of solutions like unique continuation property and analyticity.