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 {{harvtxt|Benjamin|1967}} and {{harvtxt|Ono|1975}}.
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
References
{{reflist}}
Sources
- {{citation
| last = Benjamin | first = T. Brooke | authorlink = Brooke Benjamin
| doi = 10.1017/s002211206700103x
| issue = 3
| journal = Journal of Fluid Mechanics
| page = 559
| title = Internal waves of permanent form in fluids of great depth
| volume = 29
| year = 1967| bibcode = 1967JFM....29..559B | s2cid = 123065419 }}
- {{citation
| last = Ono | first = Hiroaki
| doi = 10.1143/JPSJ.39.1082
| issue = 4
| journal = Journal of the Physical Society of Japan
| mr = 0398275
| pages = 1082–1091
| title = Algebraic solitary waves in stratified fluids
| volume = 39
| year = 1975| bibcode = 1975JPSJ...39.1082O
}}
External links
- [http://felix.physics.sunysb.edu/~abanov/Solitons/solitons_main.html Benjamin-Ono equations: Solitons and Shock Waves]
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Category:Nonlinear partial differential equations
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