Abundant explicit solutions for the M-fractional coupled nonlinear Schrödinger–KdV equations

Abstract

In this study, the famous fractional generalized coupled cubic nonlinear Schrödinger–KdV equations arising in many domains of physics and engineering such as depicting the propagation of long waves in dispersive media and the dynamics of short dispersive waves for narrow-bandwidth packet have been investigated. We propose two significant methods named the modified (Gʹ/G, 1/G)-expansion method and the Gʹ/(bGʹ + G + a)-expansion method. After utilizing these two efficient techniques, many types of explicit soliton pulse solutions including the well-known bell-shape bright soliton pulse, the kink and anti-kink dark solitons pulse, the mixed bright-dark soliton pulse, the W-shaped soliton pulse, the periodic waves pulse, and the blow-up soliton pattern solutions are obtained. If we select different values of the frequency, coefficients and orders, the dynamic properties and physical structures of these solutions are discussed, these important results can help us to further understand the inner characteristic of the model.

Overtaking interaction of electron-acoustic solitons in Saturn’s magnetosphere

“…The future work could include physical effects like collisional force between the particles inside the plasma or nonplanar geometrical effects which make the resulting nonlinear evolution equations nonintegrable. [65][66][67] For solving and analyzing these evolution equations, some approximate techniques such as the family of the homotopy perturbation method (HPM), 68,69 the family of Adomian decomposition method (ADM), 70 and many other numerical methods 71 could be gainfully employed.…”

On the oblique electrostatic waves in a dusty plasma with non-Maxwellian electrons for Saturn’s magnetosphere

“…Future work: In this plasma model, if the nonplanar geometrical effect, the collisional force between the plasma particles or the higher-order perturbation is/are considered, [39][40][41] we will get some non-integrable evolution equations which can be solved using some semi-analytical and numerical approaches. [42][43][44][45][46][47][48]…”

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

“…Up to now, many powerful methods for this subject have been built: the improved F-expansion method [8], the G′/G-expansion method [9], the improved G′/G 2 -expansion method [10], the improved (m + G′/G)-expansion method [11], the (G′/G, 1/G)-expansion method [12], the improved extended Tanh technique [13], the subequation technique [14], the Sine-Gordon expansion method [15], the EXP (−φðξÞ) technique [16], the Bäcklund transformation method [17], the Darboux transformation method [18], the Hirota bilinear method [19], the first integral method [20], the Jacobi elliptic function expansion method [21], the Lie symmetry method [22], the new Kudryashov method [23], etc. [24][25][26][27][28][29][30].…”