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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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Modified KdV equation vt + vxxx + 6v2vx= 0

The modified KdV equation differs from the original KdV equation in the last nonlinear term only. This, however, causes several substantial differences; the superficial similarity is rather inessential. On the other hand, these two equations are linked at a deeper level by the so called "Miura transformation".