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Effects of finite curvature on soliton dynamics in a chain of nonlinear oscillators

Peter L. Christiansen·Yuri B. Gaididei·Serge F. Mingaleev
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Abstract

We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a number of qualitative effects. In particular, the energy of nonlinear localized excitations centered on the bending decreases when curvature increases, i.e. bending manifests itself as a trap for excitations. Moreover, the potential of this trap is double-well, thus leading to a symmetry breaking phenomenon: a symmetric stationary state may become unstable and transform into an energetically favorable 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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Peter L. Christiansen, Yuri B. Gaididei, Serge F. Mingaleev. 2000-11-30. Effects of finite curvature on soliton dynamics in a chain of nonlinear oscillators. https://doi.org/10.1088/0953-8984%2F13%2F6%2F301

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