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

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.

13 pages (LaTeX) with 10 figures (EPS)

References in corpus (2)

• Curvature-induced symmetry breaking in nonlinear Schrodinger models
• Statistical mechanics of semiflexible ribbon polymers

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