Ethan Davis

Wave Patterns surrounding large-amplitude rogue waves and universality

This work studies wave patterns generated around large-amplitude rogue wave formations and their universal character. The project focuses on developing analytical techniques to rigorously characterize the asymptotic behavior of solutions to nonlinear wave models in the regime where the rogue wave amplitude becomes large. By extending existing approaches to a broader class of equations, this work aims to deepen our understanding of nonlinear wave dynamics and to identify universal structures that arise independently of initial conditions. The techniques developed in this project provide tools applicable to related problems in mathematical physics and the study of extreme wave phenomena.