Dimitri J. Frantzeskakisdjf

Faculty of Physics, School of Science
University of Athens
Panepistimiopolis, Zografos
157 84 Athens, Greece



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.