Minggu, 30 November 2008

About Diederik Korteweg and Gustav de Vries

Diederik Korteweg is a dutch mathematician. Diederik Korteweg's father is a judge in 's-Hertogenbosch in the south of The Netherlands.His father send to school him in a military academy.But Diederik Korteweg feel is not be balmy learnt over there.So,he decided to make against a military career and, making the first of his changes of direction, he began his studies at the Polytechnical School of Delft.Because his love of mathematics,he decided to concentrated to mathematics.And than he become a teacher in a high school.One of his students is Gustav de Vries.
Gustav de Vries is a dutch mathematician.Gustav de Vries with Diederik Korteweg discovered the Korteweg-de Vries equation (KdV equation).
The history of the KdV equation started with experiments by John Scott Russell in 1834, followed by theoretical investigations by Lord Rayleigh and Joseph Boussinesq around 1870 and, finally, Korteweg and De Vries in 1895.
The KdV equation has several connections to physical problems. In addition to being the governing equation of the string in the Fermi–Pasta–Ulam problem in the continuum limit, it approximately describes the evolution of long, one-dimensional waves in many physical settings, including:
• shallow-water waves with weakly non-linear restoring forces,
• long internal waves in a density-stratified ocean,
• ion-acoustic waves in a plasma,
• acoustic waves on a crystal lattice,
• and more.
The KdV equation can also be solved using the inverse scattering transform such as those applied to the non-linear Schrödinger equation.

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