Taras I. Lakoba's Home page
I am a Professor at the Department of Mathematics and
Statistics
of the University of Vermont.
Currect projects:
- Eficient iteration methods for Hartree-Fock (multi-plarticle) equations.
- Multi-channel all-optical processing
and regeneration
of amplitude-
and phase-modulated optical signals. This project was done in
collaboration with the experimental group of Prof. Michael
Vasilyev
from the University of Texas at Arlington.
Past projects:
- Development of higher-order schemes for the Method of characteristics for coupled-mode equations.
- Stability of numerical methods for nonlinear PDEs beyond the
von Neumann analysis and "principle of frozen coefficients"
(specifically, for the Split-step method and Method of characteristics).
- Numerical modeling
of
electromagnetic wave scattering by small particles randomly
distributed in a volume, as well as by rough
surfaces. The specific application has been lighting by
LEDs.
- Iteration methods for finding
stationary solitary waves of nonlinear evolution equations.
- Pulse
propagation in optical fibers
(nonlinearity, noise accumulation, etc).
- Perturbation theory for nonlinear wave
equations.
- The Inverse Scattering
Transform method for soliton equations.