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.