  We construct domain-wall skyrmion chains and domain-wall bimerons in chiral
magnets with an out-of-plane easy-axis anisotropy and without a Zeeman term
coupling to a magnetic field. Domain-wall skyrmions are skyrmions trapped
inside a domain wall, they are present in the ferromagnetic (FM) phase of a
chiral magnet with an out-of-plane easy-axis anisotropy. In this paper, we
explore the stability of domain-wall skyrmions in the FM phase and in a chiral
soliton lattice (CSL) or spiral phase, which is a periodic array of domain
walls and anti-domain walls arranged in an alternating manner. In the FM phase,
the worldline of a domain-wall skyrmion is bent to form a cusp at the position
of the skyrmion. We describe such a cusp using both an analytic method and
numerical solutions, and find a good agreement between them for small DM
interactions. We show that the cusp grows toward the phase boundary with the
CSL, and eventually diverges at the boundary. Second, if we put one skyrmion
trapped inside a domain wall in a CSL, it decays into a pair of merons by a
reconnection of the domain wall and its adjacent anti-domain wall. Third, if we
put skyrmions and anti-skyrmions alternately in domain walls and anti-domain
walls, respectively such a chain is stable.
