  We study topological properties of one-dimensional nonlinear bichromatic
superlattices and unveil the effect of nonlinearity on topological states. We
find the existence of nontrivial edge solitions, which distribute on the
boundaries of the lattice with their chemical potential located in the linear
gap regime and are sensitive to the phase parameter of the superlattice
potential. We further demonstrate that the topological property of the
nonlinear Bloch bands can be characterized by topological Chern numbers defined
in the extended two-dimensional parameter space. In addition, we discuss that
the composition relations between the nolinear Bloch waves and gap solitions
for the nonlinear superlattices. The stabilities of edge solitons are also
studied.
