Modified Korteweg-De Vries equation

The modified Korteweg–de Vries (KdV) equation is an integrable nonlinear partial differential equation:


 * $$u_t+u_{xxx}+\alpha u^2 u_x=0 \, $$

where $$\alpha$$ is an arbitrary (nonzero) constant.

This is a special case of the Gardner equation.