Solitonic wave Structures and Stablility Analysis for the M-fractional Generalized Coupled Nonlinear SchröDinger-KdV Equations

The M-fractional generalized coupled nonlinear Schrödinger-Korteweg–de Vries (NLS-KdV) equations which arise as an equation for the interaction between long and short nonlinear waves are investigated in the present paper. The two efficient techniques, namely, the modified Jacobi elliptic function expansion and the unified Riccati equation expansion are utilized to obtain optical solitonic wave solutions and Jacobi elliptic function solutions. A comparative analysis is represented by graphically to study the effect of the fractional order on the acquired solutions. Furthermore, the modulation instability of the equation is examined by using the standard linear stability analysis. The effect of numerous parameters on the modulation instability gain spectrum is also studied.