Summary
Solitary waves that maintain their shape as they propagate have been observed for nearly two centuries. Today, these coherent structures are known as solitons. They arise in many nonlinear wave models in mathematics and physics, and they play an important role in understanding how complex wave patterns evolve over long times. While many of their properties are understood in special exactly solvable models, their stability, interactions, and long-time behavior remain poorly understood in many physically important settings. Basic questions remain about when such structures persist, how they inte
