Solitons are nonlinear waves of finite amplitude which retain their shape after interacting with each other. They are important for many different applications including nonlinear optics, fluid dynamics, and quantum physics. Figure illustrates two exactly interacting nonlinear solitons without perturbation. Profesor Haberman has studied how solitons behave under perturbations. Recently, he has used singular perturbation methods for dynamical systems to investigate the interaction of an optical soliton with a radiation mode caused by a defect.