Stability of solitary waves

Dispersive waves, such as solutions of Schroedinger equations and KdV equations, tend to spread out in space. However, several dispersive equations with attractive nonlinearities have solutions with spatially-localized profiles which do not decay in time. They are called solitary waves, or solitons. In this colloquium, I would like to describe known results on long time dynamics of these solutions, especially their stability with initial data in the energy space H^1.

Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).