  We investigate the topological properties of one-dimensional weakly
interacting topological insulators using bosonization. To do that we study the
topological edge states that emerge at the edges of a model realized by a
strong impurity or at the boundary between topologically distinct phases. In
the bosonic model, the edge states are manifested as degenerate bosonic kinks
at the boundaries. We first illustrate this idea on the example of the
interacting Su-Schrieffer-Heeger (SSH) chain. We compute the localization
length of the edge states as the width of an edge soliton that occurs in the
SSH model in the presence of a strong impurity. Next, we examine models of two
capacitively coupled SSH chains that can be either identical or in distinct
topological phases. We find that weak Hubbard interaction reduces the ground
state degeneracy in the topological phase of identical chains. We then prove
that similarly to the non-interacting model, the degeneracy of the edge states
in the interacting case is protected by chiral symmetry. We then study
topological insulators built from two SSH chains with inter-chain hopping, that
represent models of different chiral symmetric universality classes. We
demonstrate in bosonic language that the topological index of a weakly coupled
model is determined by the type of inter-chain coupling, invariant under one of
two possible chiral symmetry operators. Finally, we show that a general
one-dimensional model in a phase with topological index $\nu$ is equivalent at
low energies to a theory of at least $\nu$ SSH chains. We illustrate this idea
on the example of an SSH model with longer-range hopping.
