Date: Monday, April 04, 2022
Location: ZOOM ID: 926 6491 9790 Virtual (4:00 PM to 5:00 PM)
Title: Uniqueness of solutions of the KdVhierarchy via Dubrovintype flows
Abstract: We consider the Cauchy problem for the KdV hierarchy  a family of integrable PDEs with a Lax pair representation involving onedimensional Schrodinger operators  under a local in time boundedness assumption on the solution.
For reflectionless initial data, we prove that the solution stays reflectionless. For almost periodic initial data with absolutely continuous spectrum, we prove that under Craigtype conditions on the spectrum, Dirichlet data evolve according to a Lipschitz Dubrovintype flow, so the solution is uniquely recovered by a trace formula. This applies to algebrogeometric (finite gap) solutions; more notably, we prove that it applies to small quasiperiodic initial data with analytic sampling functions and Diophantine frequency.
This also gives a uniqueness result for the Cauchy problem on the line for periodic initial data, even in the absence of Craigtype conditions. This is joint work with Milivoje LukiÄ‡.
A recording of the talk can be found here.
Files:
Speaker: Giorgio Young
Institution: Rice University
Event Organizer: Ahmad Barhoumi barhoumi@umich.edu
