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 Benjamin (1967) and Ono (1975).

The Benjamin–Ono equation is

${\displaystyle u_{t}+uu_{x}+Hu_{xx}=0}$

where H is the Hilbert transform.

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