My research interests are in applied mathematics of optical communications (in optical fibers and in the atmosphere), and in mathematical modeling of dynamics of phase transitions (with applications in materials science). 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 Raman scattering;
(d) 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) Light propagation in random media
(a) Propagation of partially coherent light in atmospheric turbulence;
(b) Using multiple laser beams in free space laser communication.

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

(6) Atomic processes in plasma


The focus of my research is usually on the interplay between nonlinearity and noise/disorder, using both analytical calculations and numerical simulations.