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Abba Ramadan’s Colloquium
September 5 @ 11:00 am - 12:00 pm
Title: Stability of Nonlinear Waves in Hamiltonian PDE
Abstract: Nonlinear dispersive wave equations arise as reduced mathematical models from governing equations of mathematical physics, such as the Navier-Stokes and Maxwell equations. These reduced models combine the leading-order balance between nonlinear and dispersive effects present in wave propagation. The existence and stability of coherent structures such as traveling, standing, or periodic wave solutions, and the long-time dynamics near these coherent structures are of great importance. In this talk, I will present some of the ideas (ODE and PDE theory) that one typically employs to define and study the stability of such structures. I will also discuss the models I have investigated the existence and dynamics of nonlinear waves
Bio: Abba is currently a post-doc at the University of Alabama. He received his Ph.D. in Mathematical Sciences from the University of Kansas. His research interests consist of investigating the existence and stability of solitary in the Hamiltonian dynamical system, minimizers for energies in phase separation models, the existence and stability of hollow vortices and water waves, and multidimensional front/pulse evolution in dispersively driven systems.