Key themes in Professor Ablowitz’ research are the understanding of the nonlinear wave phenomena that arise in physical problems. Mathematical techniques employed are asymptotic approximations, numerical and exact methods to obtain solutions to the underlying equations. Frequently employed are methods to solve certain nonlinear wave equations by the Inverse Scattering Transform (IST). IST allows one to construct general solutions to certain initial-boundary value problems. The problems of interest arise in a variety of physical problems. Physical applications include nonlinear optics, water waves, lattice excitations and Bose-Einstein Condensation (BEC). A special class of solutions are called solitons or solitary waves which are extremely stable localized waves.
Nonlinear wave equations, integrable nonlinear equations and solutions via the inverse scattering transform, solitons and solitary waves, mathematical modeling in fluids and nonlinear optics, mode locked lasers, optical lattices, water waves, differential and integral equations, mathematical physics