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 Camassa–Holm equation has infinite propagation speed. © 2006 Elsevier Inc. All rights reserved.