Effects of finite curvature on soliton dynamics in a chain of non-linear oscillators

We consider a curved chain of non-linear oscillators and show that the interplay of curvature and non-linearity leads to a number of qualitative effects. In particular, the energy of non-linear localized excitations centred on the bending decreases when curvature increases, i.e. bending manifests itself as a trap for excitations.

Moreover, the potential of this trap is a double-well one, thus leading to a symmetry-breaking phenomenon: a symmetric stationary state may become unstable and transform into an energetically favourable asymmetric stationary state. The essentials of symmetry breaking are examined analytically for a simplified model.

We also demonstrate a threshold character of the scattering process, i.e. transmission, trapping, or reflection of the moving non-linear excitation passing through the bending.