Discrete kink dynamics in hydrogen-bonded chains I: The one-component model

We study topological solitary waves (kinks and antikinks) in a nonlinear one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse type. This chain is used to describe the collective proton dynamics in quasi-one-dimensional networks of hydrogen bonds, where the on-site potential plays role of the proton potential in the hydrogen bond. The system supports a rich variety of stationary kink solutions with different symmetry properties. We study the stability and bifurcation structure of all these stationary kink states. An exactly solvable model with a piecewise ``parabola-constant'' approximation of the double-Morse potential is suggested and studied analytically. The dependence of the Peierls-Nabarro potential on the system parameters is studied. Discrete travelling-wave solutions of a narrow permanent profile are shown to exist, depending on the anharmonicity of the Morse potential and the cooperativity of the hydrogen bond (the coupling constant of the interaction between nearest-neighbor protons).Comment: 12 pages, 20 figure

Surface solitons at the edges of graphene nanoribbons

We demonstrate numerically that armchair graphene nanoribbons can support vibrational localized states in the form of surface solitons. Such localized states appear through self-localization of the vibrational energy along the edge of the graphene nanoribbon, and they decay rapidly inside the structure. We find five types of such solitary waves including in-plane and out-of-plane edge breathers and moving envelope solitons

Discrete breathers in carbon nanotubes

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

Effect of substrate on thermal conductivity of single-walled carbon nanotubes

We analyze numerically the thermal conductivity of single-walled carbon nanotubes placed on a flat rigid substrate. We demonstrate that the character of thermal conductivity depends crucially on the interaction between the nanotube and the substrate. In particular, we reveal that unlike the well-established anomalous thermal conductivity of isolated carbon nanotubes, the nanotube placed on a substrate demonstrates normal thermal conductivity due to the appearance of a narrow gap in the frequency spectrum of acoustic phonons