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

\( u_t+uu_x+Hu_{xx}=0 \)

where H is the Hilbert transform.
See also

Bretherton equation

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

Benjamin-Ono equations: Solitons and Shock Waves
Benjamin-Ono equation at the Dispersive PDE Wiki