My name is Fudong Wang. I am currently working as a postdoc at UCF (supervised by Alexander Tovbis). My dissertation mentor is Wen-Xiu Ma. My research interests include classical soliton theory ( inverse scattering, long-time asymptotics) and (currently) spectral theory of soliton/breather gases. Besides the integrable system, I am also interested in any fields related to the following keywords: Riemann-Hilbert problems, random matrices, orthogonal polynomial, probability theory, potential theory, asymptotic analysis, singular integral equations and approximation theory.
I am dedicated to research in mathematical physics and applied analysis. In particular, I am interested in applying analytical tools to study nonlinear integrable PDEs and to understand the physics phenomenon behind those PDEs. The Korteweg–De Vries equation (KdV) and the focusing Nonlinear Schrödinger equation (fNLS) are two important examples among them. Both KdV and fNLS are considered as universal mathematical models describing physics phenomena of nonlinear waves. Thus, many applications can be found in many other fields such as oceanography, nonlinear optical, shallow water wave, and so on. My Ph.D study mainly focuses on the long-time asymptotics of a family of integrable PDEs using some recently developed asymptotics analysis techniques (namely, matrix Riemann-Hilbert problems, nonlinear steepest descent method, $\bar\partial$-steepest descent method.). While during my postdoctoral period, I mainly consider the spectral theory arising in the study of KdV and fNLS soliton gas.