TY - JOUR
T1 - Effects of finite curvature on soliton dynamics in a chain of non-linear oscillators
AU - Christiansen, Peter Leth
AU - Gaididei, Yuri B.
AU - Mingaleev, Serge
PY - 2001
Y1 - 2001
N2 - 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.
AB - 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.
U2 - 10.1088/0953-8984/13/6/301
DO - 10.1088/0953-8984/13/6/301
M3 - Journal article
SN - 0953-8984
VL - 13
SP - 1181
EP - 1192
JO - Journal of Physics Condensed Matter
JF - Journal of Physics Condensed Matter
IS - 6
ER -