  A new procedure of trial variational wave functional is proposed for
investigating the mass renormailzation and the local structure of the ground
state of a one-dimensional quantum sine-Gordon model with linear spatial
modulation, whose ground state differs from that without modulation. The phase
diagram obtained in parameters $(\alpha \Lambda ^{-2},\beta ^{2})$ plane shows
that the vertical part of the boundary between soliton lattice phase and
incommensurate (IC) phase with vanishing gap sticks at $\beta ^{2}$ $=4\pi $,
the IC phase can only appear for $\beta ^{2}$ $\geq 4\pi $ and the IC phase
regime is enlarged with increasing spatial modulation in the case of definite
parameter $\alpha \Lambda ^{-2}$. The transition is of the continuous type on
the vertical part of the boundary, while it is of the first order on the
boundary for $\beta ^{2}>4\pi $.
