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Unsolved Problems in Mathematical Systems and Control Theory by Vincent D. Blondel, Alexandre Megretski

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Problem 7.4

Control of the KdV equation

Lionel Rosier

Institut Elie Cartan

Université Henri Poincare Nancy 1

B.P. 239

54506 Vandoeuvre-lès-Nancy Cedex

France

rosier@iecn.u-nancy.fr

1 DESCRIPTION OF THE PROBLEM

The Korteweg-de Vries (KdV) equation is the simplest model for unidirectional propagation of small amplitude long waves in nonlinear dispersive systems. It occurs in various physical contexts (e.g., water waves, plasma physics, nonlinear optics). It reads

16817

16844

2 MOTIVATION AND HISTORY OF THE PROBLEM

The KdV equation has been first introduced ...

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