PIMS Applied Mathematics Colloquium & Applied Math Seminar
Improving Archimedes: the water wave pressure problem & The stability of elliptic solutions of the focusing NLS equation
PIMS Applied Mathematics Colloquium
Date/Time: Friday, February 28th @ 3:30 PM
Location: PHYSICS 107
Speaker: Bernard Deconinck, University of Washington
Title: Improving Archimedes: the water wave pressure problem
Abstract: I will discuss a new method to recover the water-wave surface elevation from pressure data obtained at the bottom of a fluid. The new method requires the numerical solution of a nonlocal nonlinear equation relating the pressure and the surface elevation which is obtained from the Euler formulation of the water-wave problem without approximation. From this new equation, a variety of different asymptotic formulas are derived. The nonlocal equation and the asymptotic formulas are compared with both numerical data and physical experiments, demonstrating excellent agreement, significantly beyond what is obtained using Archimedes' p = ρgh
Applied Math Seminar
Date/Time: Friday, February 28th @ 9:30-10:30 AM
Location: PHYSICS 130
Speaker: Bernard Deconinck, University of Washington
Title: The stability of elliptic solutions of the focusing NLS equation
Abstract: The stability of the elliptic solutions of the focusing nonlinear Schrödinger equation (NLS) with respect to subharmonic perturbations is discussed. Using the integrability of NLS, we discuss the spectral stability of the elliptic solutions, establishing that solutions of smaller amplitude are stable with respect to larger classes of perturbations. We show that spectrally stable solutions are orbitally stable by constructing a Lyapunov functional using higher-order conserved quantities of NLS.
We hope to see you all there!
Colloquium Committee
University of Saskatchewan
Department of Mathematics and Statistics
Find us on Facebook @uofs.math.stats and Twitter @UofS_Math_Stats