SEMINAR: Stability of Nonlinear Waves in Hamiltonian PDE

Guest: Abba Ramadan, University of Alabama,

Title: Stability of Nonlinear Waves in Hamiltonian PDE (MATH)

Date/Time: December 18, 2024, 13:40

Location: FENS L062

Abstract: Nonlinear dispersive 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 for the existence and dynamics of nonlinear waves.

Bio: Dr. Abba Ramadan is an assistant professor in the Department of Mathematical Sciences at the University of Alabama, USA. He earned his B.Sc. from Gaziantep University, his M.Sc. under the supervision of Albert Erkip at Sabancı University, and his Ph.D. under the supervision of Atanas Stefanov at the University of Kansas, all in the field of Mathematical Sciences. His research interests focus on the existence and stability of solitary waves in Hamiltonian dynamical systems, minimizers of energy in phase separation models, the stability and dynamics of hollow vortices and water waves, and the evolution of fronts and pulses in dispersively driven systems.