Analytic soliton solutions for RKL equation with quadrupled power-law of self-phase modulation using modified extended direct algebraic method

The fast development of technology and science increases the demand on solving quite complicated nonlinear partial differential equations (NLPDEs) in order to simulate their physical phenomena. In the current work, the modified extended (ME) direct algebraic method is applied on the generalized Radhakrishnan–Kundu–Lakshmanan (RKL) equation with quadrupled power-law of self-phase modulation the to extract its optical solitons. Many varieties of traveling wave solutions are established like, bright solitons, dark solitons, singular solitons and combo singular-dark solitons. Some significant solutions have been graphically elaborated in a form of 2D, 3D and contour plots by selecting the appropriate parameters in order to provide a better physical illustration and understanding of the dynamical physical properties of this model.