Envelope solitons of the nonlinear discrete vertical dust grain oscillation in dusty plasma crystals.

• The vertical grain displacement model is presented. • The acquired results are given by some figures. • The modulation analysis is given. • Bright, dark and singular optical solitons are presented. The paper concerns envelope soliton propagating through the nonlinear transverse dust grain displacement in dusty plasma crystals. The work found its motivation from the recent paper of the authors [7]. To reach the goal of this study we establish the linear dispersion and the nonlinear Schrödinger equation (NLSE) by employing the quasi discrete approximation [7,13–15]. Contrary to ref. [7] , it is observed one additional regime of the formation of the dark soliton while choosing the gap frequency value (ω g ≈ 150 sec −) which is close to the experimental value given by Motcheyo et al. [7] , Tsopgue et al. To corroborate the prediction made analytically to group velocity, was confirmed by numerical and experimental studies. As, it is established that in general manner the modulated waves describing by the NLSE can be stable or unstable to the perturbation, the modulation instability of steady state have been done. Despite, that the bandwidth of the model has been reduced compared to [7,13–15] , we can say without hesitation that this work will be a capital contribution in dusty plasma crystal. [ABSTRACT FROM AUTHOR]