  We study numerically self-trapped (polaron) states of quasiparticles
(electrons, holes or excitons) in a deformable nanotube formed by a hexagonal
lattice, wrapped into a cylinder (carbon- and boron nitride-type nanotube
structures). We present a Hamiltonian for such a system taking into account an
electron-phonon interaction, and determine conditions under which the lowest
energy states are polarons.We compute a large class of numerical solutions of
this model for a wide range of the parameters. We show that at not too strong
electron-phonon coupling, the system admits ring-like localized solutions
wrapped around the nanotube (the charge carrier is localized along the nanotube
axis and uniformly distributed with respect to the azimuthal coordinate). At
stronger coupling, solutions are localized on very few lattice sites in both
directions of the nanotube. The transition from one type solution to the other
one depends on the diameter of the nanotube. We show that for the values of the
carbon nanotube parameters, the polarons have a ring-like structure wrapped
around the nanotube with a profile resembling that of the nonlinear Schrodinger
soliton.
