Seminars

Home Schools Mathematics Seminars

TITLE: [GS_M_APP] Classification of Blow-up Dynamics for the Calogero–Moser Derivative NLS

ABSTRACT: I will present recent progress on the study of finite-time blow-up dynamics for the Calogero–Moser derivative nonlinear Schrödinger equation (CM-DNLS). A central objective is to describe and ultimately classify the possible blow-up scenarios for this model. Along the way, several steps have been achieved: the construction of smooth chiral blow-up solutions (joint with Kihyun Kim, Soonsik Kwon), a soliton resolution result (joint with Soonsik Kwon), and the existence of smooth quantized blow-up solutions under symmetry restrictions (joint with Uihyeon Jeong). Building on these developments, in joint work with Uihyeon Jeong, Kihyun Kim, and Soonsik Kwon, we establish a classification of finite-time blow-up scenarios involving a single soliton for CM-DNLS. I will describe this classification result in detail and also briefly introduce some of the main ideas of the proof.