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.