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The modified Korteweg-de Vries equation. (English) Zbl 1334.35299

Summary: It is shown that the modified Korteweg-de Vries equation can be solved exactly by the ‘inverse scattering method’. As a special case, the \(N\)-soliton solution is obtained explicitly. It is found that an \(N\)-soliton collision in the modified Korteweg-de Vries equation is essentially the same as that in the standard Korteweg-de Vries equation; an \(N\)-soliton collision is described as the successive collisions of two solitons, and there is no effect of multiparticle collisions. Moreover, it is shown that the modified Korteweg-de Vries equation has new families of solutions.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
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