My research interests are in applied mathematics, partial differential equations, dynamical systems, mathematical physics, and applied probability. The focus of my research is usually on the interplay between nonlinearity and noise/disorder, using both analytic calculations and numerical simulations. Analytic calculations include asymptotic expansions, model reduction, and stability analysis. Numerical simulations are often based on spectral methods or finite difference methods. Following is a list of problems I have worked on:

(1) Nonlinear optics
(a) Effects of noise and disorder on optical solitons (conventional and dispersion-managed);
(b) Collisions of optical solitons and emission of continuous radiation; 
(c) Effects of Kerr nonlinearity and Raman scattering;
(d) Silicon photonics;
(e) Propagation in periodic photonic structures.

(2) Optical fiber communication systems
(a) Pulse collisions in multichannel (WDM) optical fiber communication systems;
(b) Multichannel (WDM) transmission systems as complex systems.

(3) Pattern formation
(a) Effects of noise and disorder on emerging patterns;
(b) Coarsening of pattern forming systems, fractal coarsening.

(4) Dynamical systems
N-dimensional population models and their applications in optics, chemistry, sociology, and in ... population dynamics.

(5) Light propagation in random media
(a) Propagation of partially coherent light in atmospheric turbulence;
(b) Using multiple laser beams in free space laser communication.

(6) Coarsening dynamics
(a) Ostwald ripening;
(b) Coarsening of granular matter;
(c) Fractal coarsening.

(7) Atomic processes in plasma