Shenzhen University School of Mathematical Sciences  

Liyuan Scholars Colloquium Session 158  

Title: Rogue wave universality for the focusing nonlinear Schrödinger equation

Speaker: Professor Peter Miller（University of Michigan）

Time: 10:00–12:00, December 26, 2025

Location: Room 1, Huixing Building, Yuehai Campus, Shenzhen University

Abstract: The focusing nonlinear Schrödinger (NLS) equation admits numerous solutions having the character of rogue waves.  These solutions are space-time localized perturbations of an unstable background solution, and are therefore connected with the idea of nonlinear saturation of modulational instabilities.  For sequences of rogue-wave solutions of increasingly large amplitude, it has been shown that a limiting waveform called a rogue wave of infinite order (RWIO) models the peak of the wave.  The RWIOs are themselves solutions of a focusing NLS equation in rescaled coordinates, and unlike finite-order rogue waves they are transcendental in nature.  While they can be derived as limits of sequences of rogue-wave solutions of increasing amplitude, it turns out that RWIOs appear more generally in the NLS theory as a universal model for large-amplitude highly peaked solutions of diverse origins.  After describing some of the properties of RWIO solutions, the talk will conclude with an illustration of the universality property by showing how RWIOs characterize the dispersive regularization of a family of singular solutions of the dispersionless NLS equation obtained in the 1960s by Talanov.

Speaker Profile: Professor Miller studied with C. D. Levermore at the University of Arizona (Tucson), where he received his PhD in 1994.  He held postdoctoral positions at the Australian National University (Canberra), the Institute for Advanced Study (Princeton), and Monash University (Melbourne).  He is currently Professor of Mathematics at the University of Michigan (Ann Arbor).  He is the author of more than 75 research articles, two research monographs, and a textbook on asymptotic analysis.

All faculty and students are welcome!  

School of Mathematical Sciences  

December 16, 2025