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Nonlinear dynamics of long-range diatomic chain

Author

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  • Okaly, Joseph Brizar
  • Mvogo, Alain
  • Woulaché, Rosalie Laure
  • Kofané, Timoléon Crépin

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 Schrödinger 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 Schrödinger equation allowing classical bright and dark soliton solutions.

Suggested Citation

  • Okaly, Joseph Brizar & Mvogo, Alain & Woulaché, Rosalie Laure & Kofané, Timoléon Crépin, 2020. "Nonlinear dynamics of long-range diatomic chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    • Handle: RePEc:eee:phsmap:v:541:y:2020:i:c:s0378437119320151
    DOI: 10.1016/j.physa.2019.123613
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    Cited by:

    1. Nkomom, Théodule Nkoa & Ndzana, Fabien II & Okaly, Joseph Brizar & Mvogo, Alain, 2021. "Dynamics of nonlinear waves in a Burridge and Knopoff model for earthquake with long-range interactions, velocity-dependent and hydrodynamics friction forces," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Nkomom, Théodule Nkoa & Okaly, Joseph Brizar & Mvogo, Alain, 2021. "Dynamics of modulated waves and localized energy in a Burridge and Knopoff model of earthquake with velocity-dependant and hydrodynamics friction forces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).

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