Kinetic behavior of subsonic solitary wave in graphene nanoribbon

In this paper we investigate the kinetic behavior of subsonic solitary waves in graphene nanoribbons by means of molecular dynamics simulations. Unlike generating the supersonic solitary waves by a strong excitation, we generate three types of subsonic solitary waves by absorbing the thermal fluctuations in the armchair and zigzag graphene nanoribbons. They are localized in longitudinal, transverse, or coupled in both velocity directions with propagation speeds lower than the sound speeds. Their typical width is about 20-80 nm, which is much longer than the width of the supersonic solitary wave. More interestingly, they correspond to energy cavities rather than energy summits in the energy distribution due to the deformation in the density distribution. The observation of subsonic solitary waves with energy cavities implies the numerical evidence of dark solitary waves in graphene. Furthermore, the collisions between two solitary waves are investigated. The nonlinear phase shift only occurs during the collision of two solitary waves localized in the same velocity direction. We hope our results shed light on understanding the particular nonlinear properties of graphene.