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We address a simple model allowing the existence of domain walls withorientational moduli localized on them. Within this model, we discuss ananalytic solution and explore it in the context of previously known results. Wediscuss the existence of one-dimensional domain walls localized ontwo-dimensional ones, and construct the corresponding effective action. In thelow-energy limit, which is the $\mathbb{O}(3)$ sigma-model, we discuss theexistence of skyrmions localized on domain walls, and provide a solution for askyrmion configuration, based on an analogy with instantons. We performsymmetry analysis of the initial model and of the low-energy theory on thedomain wall world volume.

Strings and skyrmions on domain walls