the camassa–holm equation is an integrable system. integrability means that there is a change of variables (action-angle variables) such that the evolution equation in the new variables is equivalent to a linear flow at constant speed. this change of variables is achieved by studying an associated isospectral/scattering problem, and is reminiscent of the fact that integrable classical hamiltonian systems are equivalent to linear flows at constant speed on tori. the camassa–holm equation is integrable provided that the momentum