Bernard Deconinck : Cnoidal wave solutions of the KdV equation are linearly stable.

Posted by , part of the Departmental Colloquium.

At

March 20, 2008, 3 p.m.

In

SEO 636

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.