Areas of Interest
My primary research area deals with nonlinear waves and coherent structures, an area that combines analysis, applied mathematics, and concrete physical applications. My research activity mainly focuses on the inverse scattering transform (IST) for continuous and discrete integrable systems, a mathematical technique that allows to solve the initial value problem for certain nonlinear equations. I have also addressed issues of solvability for the nonlinear Schrödinger equation, by identifying function spaces in which the direct and inverse problems are well posed. I have co-authored a monograph on nonlinear Schrödinger systems. Over the past decade, I have worked and published on mathematical techniques for solving the initial value problem for nonlinear 2+1 dimensional PDEs with potentials that do not decay at spatial infinity. Most recently, I have been working on the IST for multicomponent nonlinear Schrödinger systems with nonvanishing boundary conditions.
- MS in Mathematics, University of Salento, Italy (2010)
- PhD in Physics, University of Lecce, Italy (1999)
- MS in Physics, University of Lecce, Italy (1996)