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Generalization of the modified KdV equation to a multi-component system, that is expressed by (∂ uᵢ)/(∂ t) + 6 (∑j,k=0M-1 Cⱼₖ uⱼ uₖ) (∂ uᵢ)/(∂ x) + (∂³ uᵢ)/(∂ x³) = 0, i=0, 1, ..., M-1, is studied. We apply a new extended version of the inverse scattering method to this system. It is shown that this system has an infinite number of conservation laws and multi-soliton solutions. Further, the initial value problem of the model is solved.
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A 1998 study studied this question.
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