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In mathematics, the '''Benjamin–Ono equation''' is a nonlinear partial [[integro-differential equation]] that
describes one-dimensional [[internal wave]]s in deep water.
It was introduced by {{harvtxt|Benjamin|1967}} and {{harvtxt|Ono|1975}}.
 
The Benjamin–Ono equation is
:<math>u_t+uu_x+Hu_{xx}=0</math>
where ''H'' is the [[Hilbert transform]].
 
==References==
*[[Brooke Benjamin|T. B. Benjamin]], Internal waves of permanent form in fluids of great depth, J. Fluid Mech. 29 (1967), 559-562.
*[[Hiroaki Ono|H. Ono]], Algebraic solitary waves in stratified fluids, J. Phys.Soc. Japan 39 (1975), 1082-1091.
 
==External links==
*[http://felix.physics.sunysb.edu/~abanov/Solitons/solitons_main.html Benjamin-Ono equations: Solitons and Shock Waves]
*{{dpde|Benjamin-Ono equation}}
 
{{DEFAULTSORT:Benjamin-Ono equation}}
[[Category:Partial differential equations]]
 
 
{{mathapplied-stub}}

Revision as of 16:51, 11 September 2013

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 Template:Harvtxt and Template:Harvtxt.

The Benjamin–Ono equation is

where H is the Hilbert transform.

References

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

External links


Template:Mathapplied-stub