Project Grant 2204702

This three-year, $219,298 project grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports collaborative research on the theoretical understanding and computational modeling of collapse phenomena and rogue waves. The University of Massachusetts Amherst will lead the research effort to reformulate underlying mathematical models of nonlinear differential equations and provide a unified analytical approach for studying self-similar solutions that describe both collapse events and extreme waves. The project aims to advance insights into the mechanisms and reduced descriptions of potentially catastrophic focusing in prototypical models, as well as the formation, prediction, and analysis of abnormal waves in continuous and discrete systems. It will offer research training and explore a recently derived normal form for self-focusing central dispersion wave models. Corroborating numerical simulations and collaboration with experimentalists are also included. The results are expected to further the goals of the NSF program to strengthen the nation's scientific enterprise through increased fundamental knowledge in mathematics and physics.