Benjamin–Ono equation

In mathematics, the Benjamin–Ono equation is a nonlinear partial integro-differential equation that describes one-dimensional internal waves in deep water. It was introduced by and.

The Benjamin–Ono equation is
 * $$u_t+uu_x+Hu_{xx}=0$$

where H is the Hilbert transform.

It possesses infinitely many conserved densities and symmetries; thus it is a completely integrable system.