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Multi-soliton Dynamics for Dispersive Partial Differential Equations

US NSF grant open #nsf-2600717

Summary

The natural world is governed by wave equations: the electricity on a circuit board, the light in fiber-optic cables, the elementary particles inside atoms, and even the black hole in the center of the galaxy all propagate by wave dynamics. Though ubiquitous, wave-type equations are far from well-understood. The goal of this project is to understand how waves are affected by interference with themselves or with their environment. The research seeks to learn when and why some waves disperse, other waves persist, and still others collapse. Knowing how waves behave drives technological progress -

Multi-soliton Dynamics for Dispersive Part…
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