Partial differential equations

Whitham equation

In mathematical physics, the Whitham equation is a non-local model for non-linear dispersive waves. The equation is notated as follows : 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. Wave breaking – bounded solutions with unbounded derivatives – for the Whitham equation has recently been proven. For a certain choice of the kernel K(x − ξ) it becomes the Fornberg–Whitham equation. (Wikipedia).

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Wavenumber | Nondimensionalization | Average | Wave | Series expansion | Dirac delta function | Integro-differential equation | Derivative | Fourier transform | Peakon