Analysis of Partial Differential Equations. More specifically: 1) Soliton dynamics - linear and nonlinear stability of solitary waves in dispersive models, asymptotic stability. Existence and stability of solitary waves in spatially discrete systems. Analysis of waves in PT symmetric models. 2) Local and global behavior of nonlinear dispersive PDE's - Schroedinger, wave, Klein-Gordon, Dirac, KdV, Ostrovsky/short pulse, Whitham etc. models. 3) Well-posedness, regularity and asymptotics for fluid models: Boussinesq, quasi-geostrophic equation etc.
Teaching
Teaching Overview
Undergraduate: Calculus - I, II, III; Linear algebra; Elementary ODE; Calculus of Variations; Applied PDE. Graduate: Mathematical Analysis - I, II; Measure theory; Complex Analysis; Advanced PDE; Functional Analysis I, II; Fourier analysis and PDE.