  Under investigation in this paper is the nonisospectral and variable
coefficients modified Kortweg-de Vries (vc-mKdV) equation, which manifests in
diverse areas of physics such as fluid dynamics, ion acoustic solitons and
plasma mechanics. With the degrees of restriction reduced, a simplified
constraint is introduced, under which the vc-mKdV equation is an integrable
system and the spectral flow is time-varying. The Darboux transformation for
such equation is constructed, which gives rise to the generation of variable
kinds of solutions including the double-breather coherent structure, periodical
soliton-breather and localized solitons and breathers. In addition, the effect
of variable coefficients and initial phases is discussed in terms of the
soliton amplitude, polarity, velocity and width, which might provide feasible
soliton management with certain conditions taken into account.
