Nonlinear dynamics of long-range diatomic chain

Abstract We investigate the dynamics of the long-range extension of the diatomic chain of atoms with different masses. Due to the non-analytic properties of the dispersion relation, we use the discrete derivative operator technique, together with a slow space–time variation of the amplitude. In short wavelength modes, we obtain a nonlinear Schrodinger equation with periodic space and time varying coefficients. By means of the similarity transformations method, we derive the breather- and kink-type soliton solutions. Interesting results such as the good agreement between numerical experiments and analytical solutions, and the decreasing of the amplitude, width and velocity of the moving soliton solutions with the long-range parameter were obtained. The defect mass between the two atoms of the chain makes the system periodically inhomogeneous. Accordingly, small periodic oscillations appear in the amplitude of the soliton solutions. In the homogeneous limit, the system is governed by the nonlinear Schrodinger equation allowing classical bright and dark soliton solutions.