Soliton patterns in the truncated M-fractional resonant nonlinear Schrödinger equation via modified Sardar sub-equation method

This article explores a noteworthy nonlinear model, namely the truncated M-fractional resonant nonlinear Schrödinger equation (RNLSE), incorporating a Kerr law nonlinearity. Various nonlinear phenomena in research domains like nonlinear optics, the atmospheric theory of deep water waves, quantum mechanics, plasma physics, and fluid dynamics can be formulated using the RNLSE. To gather various solitary wave solutions for the RNLSE, we utilize a modified version of the Sardar sub-equation method. Novel optical soliton solutions in trigonometric, hyperbolic, and exponential forms are derived. Visualization techniques, like 3D, 2D, density, and contour plots with different parameter values, effectively illustrate the diverse behaviors of soliton solutions. As a result, we attain an array of solutions, including bright, singular periodic, hyperbolic soliton, dark, periodic dark, combo dark–bright, compactons, kink, periodic, and singular kink soliton solutions. The method employed in this study is efficient, accurate, capable, and dependable for calculating soliton solutions in nonlinear models. We anticipate that the results obtained in this study hold significant potential for applications in optical fibers, plasma physics, nuclear physics, mathematical biosciences, and many more.