David Sattinger

Abstract:   The Korteweg-deVries equation has been used as a model for nonlinear water waves since its discovery in 1870 by Boussinesq. It works very well for low amplitude waves, but the KdV equation has waves of all amplitudes, whereas the actual physical equations have waves only below a certain amplitude and speed. In 1993 a somewhat more complicated model equation was proposed by Camassa and Holm. This equation supports traveling waves with sharp peaks, that bear some similarity to the wave of maximum height predicted by Stokes. These solutions were dubbed peakons by Camassa and Holm.

Like the Kdv equation, the Camassa Holm equation is formally integrable by the method of inverse scattering, but the associated operator is somewhat more complicated and requires different techniques. Richard Beals, Jacek Szmigielski, and I discovered that the celebrated theory of the moment problem due to Stieltjes can be used to produce exact formulas for the multipeakon solutions.

In this lecture I will give some background on water waves, the Korteweg-deVries equation, and explain how the moment problem is related to the multipeakon solutions.

Here are some directions to Northeastern University. Lake Hall and Nightingale Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street. The two halls are connected, with no well-defined boundary in between. In particular, 509 Lake Hall is on the same corridor as 544 Nightingale Hall.

There is free parking available for people coming to the colloquium at Northeastern's visitor parking. The entrance is from Columbus Avenue, right next to the parking garage.