PhD in Physics (1999), University of Lecce, Italy
The study of wave phenomena by means of mathematical models often leads to a certain class of nonlinear partial differential equations referred to as integrable systems.
My main area of research deals with nonlinear waves and integrable systems, and has concerned both the study of the integrability of certain nonlinear partial differential equations and their discretizations (differential-difference equations), and of the properties of these equations and their solutions. Specific problems that I have addressed are: the development of the Inverse Scattering Transform (IST) as a tool to solve the initial-value problem for scalar, vector and matrix continuous and discrete nonlinear Schrodinger (NLS) equations with both vanishing and nonvanishing boundary conditions at infinity; solitons and rogue wave solutions; vector soliton interactions, etc. Other integrable systems I have studied over the years include: short-pulse systems, Maxwell-Bloch equations, the Kadomtsev-Petviashvili equations in 2 spatial dimensions, etc.
I have also been interested in mathematical models for social and behavioral sciences. We have applied generalized kinetic methods and artificial neural networks to analyze and control the quality of an existing neuropsychiatric ward. Recently, we also developed a dynamical systems model for triadic reciprocal determinism, to study how a person experiences stress or traumatic events, and the interplay among coping self-efficacy, behavior and the perception of external environment.