In mathematical physics, the Whitham equation is a non-local model for non-linear dispersive waves.
This integro-differential equation for the oscillatory variable η(x,t) is named after Gerald Whitham who introduced it as a model to study breaking of non-linear dispersive water waves in 1967.
[4] Wave breaking – bounded solutions with unbounded derivatives – for the Whitham equation has recently been proven.
[5] For a certain choice of the kernel K(x − ξ) it becomes the Fornberg–Whitham equation.
Using the Fourier transform (and its inverse), with respect to the space coordinate x and in terms of the wavenumber k: