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

My fields of interest where I currently have active research and recent results are in the fields of Partial Diffrenetial Equations and Mathematical Physics. It includes the study of Soliton and other coherent state large time dynamics see publications [56,54,47,46,44,39,36,31,21,17,16] spectral and scattering theory[55,53,46,42,41,40,39,38,37,34,33,32,30,29,26,25 and more...], Many body Quantum Mechanics and Field Theory[46,40,33,32,and more] Mathematical Biology[58,52], Rigorous and applied Numerical analysis of dispersive wave equations[57], Resonance theories in QM[54,53,39,37,36,34,32,30,29,28,27,]

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].