Benjamin–Ono equation
Encyclopedia
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 and .
The Benjamin-Ono equation is
where H is the Hilbert transform
.
Integro-differential equation
An integro-differential equation is an equation which involves both integrals and derivatives of a function.The general first-order, linear integro-differential equation is of the form...
that
describes one-dimensional internal wave
Internal wave
Internal waves are gravity waves that oscillate within, rather than on the surface of, a fluid medium. They are one of many types of wave motion in stratified fluids . A simple example is a wave propagating on the interface between two fluids of different densities, such as oil and water...
s in deep water.
It was introduced by and .
The Benjamin-Ono equation is
where H is the Hilbert transform
Hilbert transform
In mathematics and in signal processing, the Hilbert transform is a linear operator which takes a function, u, and produces a function, H, with the same domain. The Hilbert transform is named after David Hilbert, who first introduced the operator in order to solve a special case of the...
.