New soliton solutions and modulation instability analysis of the regularized long-wave equation in the conformable sense

Abstract

In this manuscript, we explore the solitary soliton of the regularized long-wave (RLW) equation which involving with weedy nonlinearity effects and dispersion relations which arises in shallow water, phonon packets in crystals, plasma wave and ion auditory waves. To execute the soliton solutions, we applied the advance Exp( − φ(ξ)) expansion method and the new form of modified Kudryashov's technique with conformable derivative from the fractional RLW model. For the explanation of the nature of RLW model, we obtained some behavior such as on the obtained solitons as bell-wave, rogue wave, periodic and double-periodic waves. This article offered the effects of conformable derivative to check the stability of the obtained phenomena. To check the stability of this model, we use the modulation instability analysis also. This work has a decent sense to endorse the extensive proposal of the model. Some 3-D and 2-D plots with their graphical explanation provides this research to characterized the obtained waves of RLW model.