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, exact and numerical 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. Applications include water waves, nonlinear optics, lattice dynamics and Bose-Einstein Condensation (BEC). A special class of solutions are called solitons or solitary waves which are robust stable localized waves.
keywords
Nonlinear wave equations, integrable nonlinear equations and solutions via the inverse scattering transform. Solutions of these equations include solitons and solitary waves, periodic waves, and spiral waves. Applications include mathematical modeling in water waves, nonlinear optics, topological waves, inverse problems, differential and integral equations, mathematical physics.
