**Research Interests**

**-Topics of current research**__
- Spectral and scattering theory__ – Multichannel Complex Systems

The main processes of nature are described by this interaction and scattering of particles. The study of interacting complex systems with particles that can appear and disappear (as in the photoelectric processes) poses a great mathematical challenge to spectral and scattering theory.

Computational and numerical aspects of direct and inverse scattering are also involved.

__- Nonlinear Partial Differential Equations__
- Dispersive Scattering and Global Existence

Nonlinear equations which describe dispersive/hyperbolic
waves play a dominant role in fields diverse as optical and laser devices,
water and gravity waves, Complex Quantum systems and more.

The solutions of such equations often exhibit remarkably rich and complex
behavior. Of particular interest to me are systems with multichannel
asymptotic behavior in which solitary type waves as well as radiation
are present.

Computational and numerical aspects of direct and inverse scattering
are also part of this investigation

**-Research Activities
**

Large time scattering and existence for dispersive and hyperbolic equations [55,51,50,49,48,43,35,23,19,18], applications to physics[58,56,54,52].