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
have worked on:
(a) Effects of
disorder on optical solitons (conventional and
(b) Collisions of
optical solitons and emission of continuous radiation;
(c) Effects of Kerr
and Raman scattering;
(d) Silicon photonics;
(e) Propagation in periodic photonic structures.
(a) Pulse collisions in
multichannel (WDM) optical fiber communication systems;
(b) Multichannel (WDM)
transmission systems as complex systems.
(a) Effects of noise and
disorder on emerging patterns;
(b) Coarsening of pattern
forming systems, fractal coarsening.
N-dimensional population models and
their applications in optics, chemistry, sociology, and in
(5) Light propagation in random
(a) Propagation of
coherent light in atmospheric turbulence;
(b) Using multiple laser
free space laser communication.
(6) Coarsening dynamics
(a) Ostwald ripening;
(b) Coarsening of
(c) Fractal coarsening.