Nonlinear localized modes in complex chains and carbon nanotubes

We discuss the existence of spatially localized nonlinear modes in carbon nanotubes with different chiralities, and demonstrate that in nanotubes with the chirality index (m, 0) three types of localized modes can exist, namely longitudinal, radial, and twisting nonlinear localized modes. We demonstrate that only the nonlinear modes associated with the twisting oscillations are nonradiating modes, and they exist in the frequency gaps of the linear spectrum. Geometry of carbon nanotubes with the index (m, m) allows only the existence of broad radial breathers in a narrow spectral range.