In mathematics, and in particular in the theory of solitons, the Dym equation (also known as DH) is named for Harry Dym. It is Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... A soliton is a self-reinforcing solitary wave caused by nonlinear effects in the medium. ...
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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 posess the Painleve property. Dispersion can mean any of several things: A phenomenon that causes the separation of a wave into components of varying frequency. ... Nonlinear systems are mathematically represented systems whose behavior is not expressible as a linear function of its descriptors; that is, such systems are not linear. ... To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ... In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... Paul Painlevé, French politician Paul Painlevé (December 5, 1863–October 29, 1933, both at Paris, France) was a French mathematician and politician. ...
The Dym equation has strong links with the Korteweg-de Vries equation The Korteweg-de Vries equation (KdV equation for short) is the following partial differential equation for a function φ of two real variables, x and t: Its solutions clump up into solitons. ...
In mathematics, a partial differential equation (PDE) is an equation relating the partial derivatives of an unknown function of several variables.
Where ordinary differential equations have solutions that are families with each solution characterized by the values of some parameters, for a PDE the solutions often are parametrized by functions (informally put, this means that the set of solutions is much larger).
Solutions to this equation, known as harmonic functions, serve as the potentials of vector fields in physics, such as the gravitational or electrostatic fields.
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