In mathematical physics, the Degasperis–Procesi equation u t − u x x t + 2 κ u x + 4 u u x = 3 u x u x x + u u x x x {\displaystyle \displaystyle u_{t}-u_{xxt}+2\kappa u_{x}+4uu_{x}=3u_{x}u_{xx}+uu_{xxx}} is one of only two exactly solvable equations in the following family of third-order, non-linear, dispersive PDEs: u t − u x x t + 2 κ u x + u u x = b u x u x x + u u x x x, {\displaystyle \displaystyle u_{t}-u_{xxt}+2\kappa u_{x}+uu_{x}=bu_{x}u_{xx}+uu_{xxx},} where κ {\displaystyle \kappa } and b are real parameters. Wikipedia