# Math Seminar: Evolution equations with traveling wave solutions

## Mathematical Research at Notre Dame

Speaker: Professor Alex Himonas

Focusing on the Korteweg-de Vries (KdV) equation and the Camassa-Holm (CH) equation, we shall present a few ideas and techniques for solving partial differential equations. KdV was derived in 1895 as a model of long water waves propagating in a channel. Since then it has reappeared in many other areas of mathematics and its applications and it has been a favorite subject of study by mathematicians of all kinds. It possesses traveling wave solutions (solitons) having many interesting properties. However, they never break! The search for a water wave equation having traveling wave solutions that break led to the discovery of the CH equation.

Originally published at math.nd.edu.