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
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Kortweg and De Vries (KdV) equation and integrable systems
Elasticity equations
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