Korteweg-de Vries-Burgers' equation

The Korteweg-de Vries–Burgers equation is a nonlinear partial differential equation:


 * $$u_t+\alpha u_{xxx} + uu_x - \beta u_{xx}=0. $$

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.

The modified KdV-Burgers equation can be written as:


 * $$u_t+ a u_{xxx} + u^2u_x - b u_{xx}=0. $$