Bingyu Zhang

Analysis and Control of Nonlinear Dispersive Waves

Grounded in mathematics yet broadly relevant, this work examines how boundaries shape systems, how stability emerges or fails, and how local actions produce global effects. Waves—whether on oceans, in fiber-optic cables, or in the atmosphere—rarely travel without boundaries. Shorelines, channels, and engineered structures shape how they move, interact, and dissipate. Understanding and guiding these behaviors is both a scientific challenge and a practical necessity, from climate modeling to telecommunications.

This aspect of this project first develops a mathematical framework to describe how boundaries influence wave behavior, showing how walls, edges, and interfaces fundamentally alter patterns. Secondly, this project focuses on control and stabilization, presenting methods we developed to steer waves, prevent instabilities, and direct energy or information efficiently.