The Coupled Modified Korteweg-de Vries Equations
Abstract
Generalization of the modified KdV equation to a multi-component system, that is expressed by (∂ ui)/(∂ t) + 6 (Σj,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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