Definition:Korteweg-de Vries Equation
Jump to navigation
Jump to search
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