Stochastic partial differential equations (SPDEs): Existence and uniqueness, wave propagation in dispersive and nonlinear medium, random perturbations.
Asymptotic analysis: Approximation diffusion theory, weak convergence of probability measures.
Stochastic numerical analysis: Strong order of convergence for nonlinear SPDEs, conservative schemes, numerical simulations.
Nonlinear optics: Birefringence, polarization mode dispersion (PMD), soliton propagation, rogue waves in birefringent fibers.
Monte Carlo methods: Adaptive multilevel splitting for rare events simulations.
Water waves equation. To learn more.