Speaker: Jonathan Lottes, SUNY Buffalo
Date: December 3, 2020
Title: The focusing nonlinear Schrödinger equation with nontrivial boundary conditions: Inverse scattering and interactions between solitons and dispersive shocks
Abstract: The inverse scattering transform was developed for the focusing nonlinear Schrödinger equation in 1972 for rapidly decaying potentials. More recent work has treated various classes of potentials with nonzero boundary conditions. In this talk I present the inverse scattering transform for potentials with counterpropagating wave boundary conditions. This includes a discussion on the solvability of the Riemann-Hilbert problem formulated for the inverse problem. The talk concludes with consideration of the interactions between solitons and dispersive shocks for potentials in this class. This work is in collaboration with Gino Biondini (SUNY Buffalo) and Dionyssis Mantzavinos (University of Kansas).