The Kaup-Brauer System and a 2+1 Dimensional Generalization
The equations for surface waves for an inviscid and irrotational fluid in a narrow channel has a Hamiltonian formulation in which the canonical variables are the surface elevation and hydrodynamic potential on the surface. Applying a long wave approximation to these Hamiltonian equations naturally leads to a completely integrable Hamiltonian system of PDEs called the Kaup—Brauer system. Complete integrability allows one to find solutions to the Kaup—Brauer system using the dressing method, and the derivation of this method naturally leads to 2+1 dimensional generalization of the Kaup—Brauer system that preserves integrability.
(Bagels and refreshments will be served.)