The study of new optical soliton solutions to the time-space fractional nonlinear dynamical model with novel mechanisms

Abstract

In this work, we successfully employ two constructive mathematical tools such as the extended rational sine-cosine/sinh-cosh and novel Φ6-expansion model techniques, for obtaining different types of optical solitons and other solutions to the (2+1)-dimensional time-space fractional nonlinear Schrodinger (NLS) equation within the modified Riemann–Liouville derivatives. Solitary wave, dark, singular, and their combined solutions are retrieved. Moreover, hyperbolic, trigonometric, plane wave periodic wave, and Jacobi elliptic function solutions are also derived. The novelty of the obtained solutions is revealed by comparing them with the previous finding. By selecting suitable parametric values, numerical simulation and physical interpretations of the achieved outcomes are manifested with interesting figures presenting the meaning of the acquired results. The novel approaches are used through the symbolic computations impart a dynamical and potent mathematical implement for solving various benevolent nonlinear wave problems. The results suggest that these constructing techniques are concise, direct, efficient, and straightforward. The resulting solutions are novel, intriguing, and potentially helpful for understanding energy transit and diffusion processes in mathematical models of several disciplines of interest, including telecommunication, engineering, mathematical biology, mathematical physics, and nonlinear optics etc.