Analytical soliton solutions of the fractional order dual-mode nonlinear schrodinger equation with time-space conformable sense by some procedures

Abstract

This paper considers the fractional order dual-mode nonlinear Schrodinger equation (FDMNLSE) with cubic law nonlinearity. The FDMNLSE interprets the concurrent propagation of two-mode waves instead of a single wave. Throughout this work, the fractional derivative is given in terms of time and space conformable sense. The FDMNLSE introduces three physical parameters: dispersive factor, phase speed, and nonlinearity. This new model has many applications in nonlinear physics and fiber optics. We will use two methods to get new optical solutions: the generalized exponential rational function method (GERFM) and the functional variable method (FVM). Using the GERFM, we get unique wave solutions in the forms of shock wave solutions, singular soliton solutions, singular periodic waves, and exponential function solutions. Thanks to FVM, we reach bright optical soliton solutions, singular optical soliton solutions, and periodic singular wave solutions, and the restraint conditions for solutions are reported. The analytical outcomes are supplemented with numerical simulations of the got solutions to understand the dynamic behavior of obtained solutions. The results of this study may have a high-importance application while handling the other nonlinear partial differential equations (NLPDEs).