KTH/SU Mathematics Colloquium
05-09-28
Richard Beals, Yale University
The KdV and Camassa-Holm equations
The well-known KdV equation was proposed in 1895
to describe long waves in shallow water. It is now known
to have explicit solutions (multi-solitons) with interesting
interactions, computable in an unexpected way.
The same is true of an equation proposed much more recently:
the Camassa-Holm equation. The C-H special solutions
(peakons, antipeakons) have even more interesting interactions.
They come from finite-dimensional Hamiltonian systems and can
be calculated explicitly, but in a completely different way
from KdV.