For more information about this meeting, contact Victor Nistor.
|Title:||Evolution of water waves on finite depth with variable bathymetry|
|Seminar:||CCMA Luncheon Seminar|
|Speaker:||Diane Henderson, Penn State Mathematics|
|Much of the study of nonlinear water waves is focused on either shallow-water waves, governed by the KdV and KP equations; or deep-water waves, whose envelopes are governed by the nonlinear Schroedinger (NLS) equation. KdV, KP and NLS are of great interest mathematically - they are nonlinear PDEs that are integrable; and physically - they arise in may other physical systems. The in-between region, with uniform depth, is governed by the Davey-Stewartson (DS) equations, which do not share the magical property of integrability. However, for the special case of wave propagation in one horizontal dimension, the DS equations reduce to an NLS-type equation. If the depth is non-uniform, then the coefficients are variable and a new term arises. Here, we make the connection between that term and previous work on the dissipative NLS equation. We find an exact solution to the DS equations with variable bathymetry and study its stability. And we use asymptotics to find a periodic (envelope) solution to investigate the surfers' claim that "every 7th wave is the largest".|
Room Reservation Information
|Date:||03 / 23 / 2012|
|Time:||12:20pm - 01:30pm|