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Waves on Wednesday Seminar Series

Wednesday, October 19,  2005, 10:00 am
Cullimore 611
New Jersey Institute of Technology

Recurrence in the Korteweg-de Vries equation?

D. Trubatch

Department of Mathematical Sciences

US Military Academy at West Point

Abstract

The numerically-observed near-recurrence of the initial value in the periodic Korteweg-de Vries equation (KdV) has been explained in terms of the solitons of KdV. However, other numerical simulations of KdV with higher-order accuracy methods do not show recurrence under the same conditions, even though these schemes capture the individual solitons with greater accuracy. Moreover, in schemes that do show recurrence, a decrease in the grid size may not improve the observed recurrences. These observations bring into question the generally understood mechanism of the recurrence. Also, these simulations reveal some other interesting phenomena in the dynamics of KdV approximations.