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.

See also[]

• Bretherton equation

References[]

• Benjamin, T. Brooke (1967), "Internal waves of permanent form in fluids of great depth", Journal of Fluid Mechanics, 29 (03): 559, doi:10.1017/s002211206700103x
• Ono, Hiroaki (1975), "Algebraic solitary waves in stratified fluids", Journal of the Physical Society of Japan, 39 (4): 1082–1091, doi:10.1143/JPSJ.39.1082, MR 0398275

External links[]

• Benjamin-Ono equations: Solitons and Shock Waves

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