  We comprehensively investigate gap solitons and Bloch waves in
one-dimensional nonlinear periodic systems. Our results show that there exists
a composition relation between them: Bloch waves at either the center or edge
of the Brillouin zone are infinite chains composed of fundamental gap
solitons(FGSs). We argue that such a relation is related to the exact relation
between nonlinear Bloch waves and nonlinear Wannier functions. With this
composition relation, many conclusions can be drawn for gap solitons without
any computation. For example, for the defocusing nonlinearity, there are $n$
families of FGS in the $n$th linear Bloch band gap; for the focusing case,
there are infinite number of families of FGSs in the semi-infinite gap and
other gaps. In addition, the stability of gap solitons is analyzed. In
literature there are numerical results showing that some FGSs have cutoffs on
propagation constant (or chemical potential), i.e. these FGSs do not exist for
all values of propagation constant (or chemical potential) in the linear band
gap. We offer an explanation for this cutoff.
