Definition:Korteweg-de Vries Equation

Definition

The Korteweg-de Vries equation is the partial differential equation:

$\dfrac {\partial y} {\partial t} + \dfrac {\partial^3 y} {\partial x^3} + 6 y \dfrac {\partial y} {\partial x} = 0$

where $t$ denotes time and $x$ denotes a space variable.

The Korteweg-de Vries equation is classified as an integrable system.

Also see

• Results about the Korteweg-de Vries equation can be found here.

Source of Name

This entry was named for Diederik Johannes Korteweg and Gustav de Vries.

Historical Note

The Korteweg-de Vries equation was first introduced by Joseph Valentin Boussinesq in $1877$.

It was later rediscovered by Diederik Johannes Korteweg and Gustav de Vries in $1895$.

A solution to this equation is a soliton.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): integrable system