Partial Differential Equations in Applied Mathematics (Dec 2021)
A short overview of solitons and applications
Abstract
Solitons are solitary waves that maintain their shape and speed while propagating with constant velocity. They are ubiquitous in nature and have many applications in nonlinear dynamics. In this project, we give a brief historical overview of solitons. We also discuss solitary, traveling wave solutions of the classical wave equation and the famous KdV equation. Finally, we highlight a few important theoretical and physical applications of solitons.
