Some Novel Optical Solutions for the Generalized M -Fractional Coupled NLS System

Abstract

In this work, some novel optical solutions for the ( $1+1$ )-dimensional generalized $M$ -fractional coupled nonlinear Schrödinger system (GMFCNLS) arising in ocean engineering, plasma waves, and nonlinear optics have been investigated. After utilizing a modified ( $G^{\prime }/G,1/G$ )-expansion method and the $G^{\prime }/\left(b{G}^{\prime }+G+a\right)$ -expansion method, many types of novel optical solutions including the bell-shape soliton solutions, the blow-up solutions, the periodic wave solutions, and the mixed solitary wave solutions are obtained; if we select different values of wave velocity, coefficients, and orders, the dynamic properties and physical structures of these optical solutions are simulated and discussed, which can help us to further understand the inner structure of the system.