The Benjamin-Ono equation is a nonlinear partial integro-differential equation. It was introduced by Benjamin (1967) and Ono (1975) as an equation describing one-dimensional internal waves in deep water.

The Benjamin-Ono equation has a form where is the Hilbert transform.

It is a soliton equation and can be solved by an inverse scattering transform.

The Benjamin-Ono equation has a form where is the Hilbert transform.

It is a soliton equation and can be solved by an inverse scattering transform.

References:

- [1] T. Benjamin, Internal waves of permanent form in fluids of great depth, J. Fluid Mech. 29 (1967), 559-562.
- [2] H. Ono, Algebraic solitary waves in stratified fluids, J. Phys.Soc. Japan 39 (1975), 1082-1091.