Dym equation
In mathematics, and in particular in the theory of solitons, the Dym equation, also known as HD, is
- ut = u3uxxx.
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.