Determining form and data assimilation algorithm for the weakly damped and driven Korteveg-de Vries equation-Fourier modes case

We show that the global attractor of a weakly damped and driven Korteweg–de Vries equation (KdV) is embedded in the long-time dynamics of an ordinary differential equation called a determining form. In particular, there is a one-to-one identification of the trajectories in the global attractor of the damped and driven KdV and the steady state solutions of the determining form. Moreover, we analyze a data assimilation algorithm (down-scaling) for the weakly damped and driven KdV. We show that given a certain number of low Fourier modes of a reference solution of the KdV equation, the algorithm recovers the full reference solution at an exponential rate in time.


Publication Date:
Aug 01 2017
Date Submitted:
Aug 10 2018
Pagination:
287-317
ISSN:
1468-1218
Citation:
Nonlinear Analysis: Real World Applications
36
Note:
A freely accessible, full text version is available using the link(s) in External Resources.
External Resources:




 Record created 2018-08-10, last modified 2019-04-03


Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)