Korteweg–de Vries–Burgers equation

The Korteweg–de Vries–Burgers equation is a nonlinear partial differential equation: u t + α u x x x + u u x − β u x x = 0. {\displaystyle u_{t}+\alpha u_{xxx}+uu_{x}-\beta u_{xx}=0.} The equation gives a description for nonlinear waves in dispersive-dissipative media by combining the nonlinear and dispersive elements from the KdV equation with the dissipative element from Burgers' equation.