Abstract
We study large-amplitude oscillations of carbon nanotubes with chiralities (m, 0) and (m, m) and predict the existence of spatially localized nonlinear modes in the form of discrete breathers. In nanotubes with the index (m, 0) we find three types of discrete breathers associate with longitudinal, radial, and torsion anharmonic vibrations, however only the twisting breathers are found to be nonradiating nonlinear modes which survive in a curved geometry described by a three-dimensional microscopic model and remain long-lived modes even in the presence of thermal fluctuations.