Kortweg and De Vries (KdV) equation and integrable systems
Partial differential equations
Article REF: AF191 V1
Kortweg and De Vries (KdV) equation and integrable systems
Partial differential equations

Authors : Claude BARDOS, Thierry PAUL

Publication date: October 10, 2010 | Lire en français

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5. Kortweg and De Vries (KdV) equation and integrable systems

5.1 Context

The origin of the KdV equation goes back to an observation made by Scott Russell in 1865, when he noticed a surface wave on a canal created by the impact of two barges. He was struck by the stability of the wave and recounts how he was able to follow it on horseback for several kilometers. In 1895, using asymptotic methods, Kortweg and De Vries obtained the equation

∂tu+6 u ∂xu+∂x3u=0.

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