A central element in contemporary
physics is to understand and describe physical phenomena by employing detailed
mathematical models. Frequently, such models lead to large-amplitude or
nonlinear systems. Remarkably, in many cases certain prototypical
equations are found to be the fundamental underlying systems which can
be used to approximate the physical problem.

An important theme in this research
is to understand by exact, approximate and numerical methods -- and in
close collaboration with state-of-the-art experiments -- solutions to
these underlying equations and their properties. Such studies refer to
physical problems arising in nonlinear optics, the physics of ultracold
atomic gases and Bose-Einstein condensates, nonlinear metamaterials,
etc. The main focus is on a special class of solutions, in the form of
coherent localized structures, namely solitons in one-dimension and vortex structures in
higher-dimensions.

Specific research areas that are studied include:

- optical
solitons and their applications in photonics and optical communications

- dynamical instabilities, solitons and vortices in
Bose-Einstein condensates

- nonlinear dynamical lattices in optical systems and
Bose-Einstein condensates

- electromagnetic phenomena in nonlinear metamaterials

This research is based on the
analysis of non-integrable, nonlinear evolution equations. These
include various perturbed versions of the nonlinear Schrodinger (NLS)
equation, the Gross-Pitaevskii (GP) equation, the Ginzburg-Landau (GL)
equation, etc. Both continuous and discrete versions -- as well as both
one- and higher-dimensional versions -- of the above equations are
studied. Special emphasis is given to analytical approximations based
on the use of various perturbation methods (multiple scales, reductive
perturbation method, perturbation theory for solitons, variational
approaches, etc), and nonlinear dynamics techniques.