Dym equation

From Biocrawler, the free encyclopedia.

In mathematics, and in particular in the theory of solitons, the Dym equation, also known as HD, is

u_t = u³u_xxx.

It is a third-order partial differential equation, and is named after Harry Dym.

The Dym equation (hereafter HD) represents a system in which dispersion and nonlinearity are coupled together. HD is a completely integrable nonlinear evolution equation that may be solved by means of the inverse scattering transform. It is interesting because it obeys an infinite number of conservation laws; it does not possess the Painlevé property.

The Dym equation has strong links to the Korteweg-de Vries equation.

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