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

where H is the Hilbert transform.

It possesses infinitely many conserved densities and symmetries; thus it is a completely integrable system.A two-parameter Miura transformation of the Benjamin-Ono equation, T.L. Bock, M.D. Kruskal, Physics Letters A, Volume 74, Issues 3–4, 12 November 1979, Pages 173-176.

See also Bretherton equation

References

Sources

External links Benjamin-Ono equations: Solitons and Shock Waves