  Generalization of the modified KdV equation to a multi-component system, that
is expressed by $(\partial u_i)/(\partial t) + 6 (\sum_{j,k=0}^{M-1} C_{jk} u_j
u_k) (\partial u_i)/(\partial x) + (\partial^3 u_{i})/(\partial x^3) = 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.
