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

Article | REF: AF191 V1

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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