Mathematics and Applications Seminar
11:00am - 12:00pm, Friday, Feb 24, 2023
MSB 318

Speaker:
Dr. Roy Choudhury
Department of Mathematics
University of Central Florida

Title: Stable Pulse Solutions of Nonlinear PDES — Spectral, Reversible Systems and Perturbative Approaches

Abstract: Stable pulse solutions of various nonlinear PDEs are of interest in multiple areas, including Nonlinear Optics, Water Waves, Chemical Reactors, social media, and many other areas of current interest. Originally local stability was determined using the spectrum of the linearized operator around a pulse solution. About two decades ago, it was realized that, in additional to regular localized pulses living within the discrete part of the spectrum, delocalized pulses with exponentially small tails could also exist embedded within the continuous spectrum, thus leading to the name ‘embedded solitons’. Further work revealed infinite families of both localized and delocalized solitary waves or pulses in different regimes of the parameter space for the linearized operator. We shall broadly review the entire area, concluding with some new families of delocalized pulses in the extended or fifth- order Korteweg-de Vries equation that governs various phenomena including table-top or flat-top waves observed both in Nonlinear Optics and controlled water wave experiments. A combination of reversible systems, perturbative and operator theory allows one to also draw conclusions about the existence and stability of both symmetric and asymmetric pulses in various parameter regimes.

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The UCF Mathematics and Applications Seminar, which takes place every Friday from 11am to 12pm in MSB 318, provides a venue for researchers to present their current work, foster new collaborations, and showcase both foundational mathematics and its applications to graduate and undergraduate students.

https://sciences.ucf.edu/math/seminar/mathematics-and-applications-seminar