Discovery of New Exact Wave Solutions to the M-Fractional Complex Three Coupled Maccari’s System by Sardar Sub-Equation Scheme

Abstract

In this paper, we succeed at discovering the new exact wave solutions to the truncated M-fractional complex three coupled Maccari’s system by utilizing the Sardar sub-equation scheme. The obtained solutions are in the form of trigonometric and hyperbolic forms. These solutions have many applications in nonlinear optics, fiber optics, deep water-waves, plasma physics, mathematical physics, fluid mechanics, hydrodynamics and engineering, where the propagation of nonlinear waves is important. Achieved solutions are verified with the use of Mathematica software. Some of the achieved solutions are also described graphically by 2-dimensional, 3-dimensional and contour plots with the help of Maple software. The gained solutions are helpful for the further development of a concerned model. Finally, this technique is simple, fruitful and reliable to handle nonlinear fractional partial differential equations (NLFPDEs).

On Multiple-Type Wave Solutions for the Nonlinear Coupled Time-Fractional Schrödinger Model

“…Additionally, Figures 10-12 present dark kink singular solitary wave, singular kink fusion solitary waves, and kink singular solitary wave solutions, respectively, each exhibiting unique characteristics, as dictated by their corresponding equations. Finally, Figures 13 and 14 provide visual representations of singular kink fusion solitary wave solutions obtained from Equations ( 42) and (43), further enriching the understanding of the complex dynamics and interactions present in the studied nonlinear system. These detailed graphical representations serve as valuable tools for elucidating the behavior and properties of the derived solutions, offering insights into the rich and varied dynamics of the nonlinear fractional-order Schrödinger model under investigation.…”

“…Ref. [43] utilized SSET to obtain exact wave solutions for a complex three-coupled Maccari's system, further highlighting its versatility. Additionally, research in [44] has integrated SSET with conformable derivatives to investigate solitary solutions for the conformable fractional Klein-Gordon equation with high-order non-linearity.…”

Noise effect on soliton phenomena in fractional stochastic Kraenkel-Manna-Merle system arising in ferromagnetic materials

“…Among these investigations, solitons in the setting of Nonlinear FPDEs (NFPDEs) have long captivated physicists and mathematics professionals alike. Numerous analytical techniques, such as the the Sardar sub-equation method 10 , tan-function method 11 , the (G’/G)-expansion approach 12 , the Khater method 13 , the sub-equation method 14 , the Kudryashov method 15 , Jacobi elliptic function method 16 , Bilinear method 17 , mEDAM 18 method and the exp-function method 19 have been developed to elucidate and characterise soliton behaviours within NFPDEs. mEDAM 20 , 21 has emerged as a promising strategy that can be used to both NPDEs and NFPDEs.…”

Exploring Propagating Soliton Solutions for the Fractional Kudryashov–Sinelshchikov Equation in a Mixture of Liquid–Gas Bubbles under the Consideration of Heat Transfer and Viscosity

“…The fascination with solitons has piqued the curiosity of mathematicians and academics, motivating them to investigate soliton dynamics in both nonlinear FPDEs and PDEs. As a result of their efforts, several analytical methods have emerged, including the extended state-dependent differential Riccati equation approach [16], the sub-equation method [17], the (G /G)-expansion approach [18], the Sardar sub-equation method [19], the Kudryashov method [20], the modified extended tanh method [21], the exp-function method [22], the sin-Gordon method [23], and the mEDAM [24][25][26].…”