August 2017 September 2017 |

12:00 pm Wednesday, September 13, 2017 Spectral Theory Brown Bag Seminar: Existence of Solutions to the KdV Hierarchyby Tom VandenBoom (Rice University) in HBH 427- The Korteweg-de Vries (KdV) equation is a PDE which models a number of phenomena, including the propagation of waves in shallow water. Interest in the KdV equation blossomed in the 1960s with the discovery that it could be reformulated as a Lax equation involving the continuum Schroedinger operator. This led to the construction of an infinite family of KdV-like PDEs, known as the KdV hierarchy. In joint work with J. Christiansen, B. Eichinger, and P. Yuditskii, we show the global existence and almost-periodicity of classical solutions to the Cauchy problem for each KdV hierarchy for almost-periodic initial conditions under simple summability criteria on the spectral gap lengths of the associated Schroedinger operators.
Submitted by damanik@rice.edu |