Departmental Colloquium
Bernard Deconinck
University of Washington
Cnoidal wave solutions of the KdV equation are linearly stable.
Abstract: Going back to considerations of Benjamin (1974), there has been
significant interest in the question of stability for the stationary
periodic solutions of the Korteweg-deVries equation, the so-called
cnoidal waves. In this paper, we exploit the squared-eigenfunction
connection between the linear stability problem and the Lax pair for
the Korteweg-deVries equation to completely determine the spectrum
of the linear stability problem for eigenfunctions that are bounded
on the real line. We find that this spectrum is confined to the
imaginary axis, leading to the conclusion of spectral stability. An
additional completeness argument allows for a statement of linear
stability.
This is an event of the SIAM Student Chapter.
Thursday March 20, 2008 at 3:00 PM in SEO 636