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In mathematics, and in particular in the theory of solitons, the Dym equation is the third-order partial differential equation

It is often written in the equivalent form for some function v of one space variable and time

The Dym equation first appeared in Kruskal and is attributed to an unpublished paper by Harry Dym.

The Dym equation 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 obeys an infinite number of conservation laws; it does not possess the Painlevé property.

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