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Many Faces of Solitons

Kanehisa Takasaki (Kyoto University)

Entrance -- KdV equation -- Modified KdV equation -- Sine-Gordon equation

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KdV equation ut + uxxx + 6uux= 0

The Korteweg-de Vries (KdV) equation is the champion of model equations of nonlinear waves. It was studied by Korteweg and de Vries late in the 19th century as a water wave equation, and after a long period of sleep, revived as one of the most fundamental equation of soliton phenomena. In fact, it is from numerical experiments of this equation that Zabusky and Kruskal introduced the term "soliton".