Complex quadrupled-power-law nonlinearity form of Radhakrishnan-Kundu-Lakshmanan equation: novel optical soliton analysis

Abstract In this manuscript, the novel optical wave solutions to the newly developed Radhakrishnan-Kundu-Lakshmanan (NRKL) model are studied. Two analytical methods namely, the new extended generalized Kudryashov and the extended modified auxiliary equation mapping methods are used to obtain these novel solutions. Furthermore, the dynamics of the obtained solutions are analyzed thoroughly with the help of different graphical forms such as three-dimensional (3-D), contour, and two-dimensional (2-D) figures. To get the graphical view of the derived solutions, numerical values for the unknown parameters are assigned while balancing the nonlinearity with dispersion. Moreover, the characteristics analysis of the obtained solutions depict anti-kink, periodic, bright, dark-shaped periodic, anti-bell shape, bright-shaped periodic, and dark waveforms Furthermore, the practical implications of these waveforms in optical fiber transmission are profound, with the potential to influence nonlinear signal processing and advanced optical network design.