Infinite propagation speed of the Camassa-Holm equation
We use the inverse scattering transform to show that a solution of the Camassa-Holm equation is identically zero whenever it vanishes on two horizontal half-lines in the x-t space. In particular, a solution that has compact support at two different times vanishes everywhere, proving that the Carnassa-Holm equation has infinite propagation speed. (c) 2006 Elsevier Inc. All rights reserved.