Effects of finite curvature on soliton dynamics in a chain of non-linear oscillators
P. L. Christiansen, Y. B. Gaididei, and S. F. Mingaleev,
J. Phys. Condens. Matter 13, 1181-1192 (2001).
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Abstract: 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 nonlinear excitation passing through the bending.
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