Professor Ilan's research interest lies in the mathematics involved with real-world phenomena, and its application to areas such as the control of intense lasers beams and harvesting solar energy. His research uses modeling physical systems in terms of ordinary and partial differential equations. Detailed studies are obtained using functional analytic, asymptotic and perturbation analysis, and numerical computation. The over-arching goal of this research is to connect between the mathematical and physical aspects arising from these problems and make useful predictions about physical systems.