In mathematical physics, the Degasperis–Procesi equation is one of only two exactly solvable equations in the following family of third-order, non-linear, dispersive PDEs: where and b are real parameters (b=3 for the Degasperis–Procesi equation). It was discovered by Degasperis and Procesi in a search for integrable equations similar in form to the Camassa–Holm equation, which is the other integrable equation in this family (corresponding to b=2); that those two equations are the only integrable cases has been verified using a variety of different integrability tests. Although discovered solely because of its mathematical properties, the Degasperis–Procesi equation (with ) has later been found to play a similar role in water wave theory as the Camassa–Holm equation.