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The matrix-modified Korteweg-de Vries equation (MMKdV)

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The paper considers the Cauchy problem for the equation V, + ~v ' v , + v,,, = 0 with step-like initial data. It is proved by the inverse scattering method that for t + 'I_ the solution v(.Y, t ) in the neighbourhood of the leading edge breaks up into an infinite series of non-interacting solitons generated by the continuous spectrum of the respective L operator of the Lax representation.