Investigating Families of Soliton Solutions for the Complex Structured Coupled Fractional Biswas–Arshed Model in Birefringent Fibers Using a Novel Analytical Technique

Abstract

This research uses a novel analytical method known as the modified Extended Direct Algebraic Method (mEDAM) to explore families of soliton solutions for the complex structured Coupled Fractional Biswas–Arshed Model (CFBAM) in Birefringent Fibers. The Direct Algebraic Method (DAM) is extended by the mEDAM’s methodology to compute more analytical solutions that would otherwise be difficult to acquire. We use this method to derive several families of soliton solutions and examine their characteristics. We also look at how different model parameters, such as amplitude, width, and propagation speed, affect the dynamics of soliton. Our use of 2D and 3D graphics to illustrate the soliton solutions also makes it possible to see the soliton dynamics more clearly. The outcomes also demonstrate that the method suggested has proven successful in producing soliton solutions for intricate structures such as the CFBAM.

On the optical soliton solutions to the fractional complex structured (1+1)-dimensional perturbed gerdjikov-ivanov equation

“…On the other hand, analytical techniques offer the advantage of delivering exact or closed-form solutions, enabling a more thorough comprehension of the underlying mechanisms and providing efficient and exact analysis of FPDEs. To get exact solutions for nonlinear FPDEs, different analytical methods are used, including the Khater Method [15], the Exp-function method [16], the (G'/G)-expansion method [17], EDAM [18] and many other techniques [19][20][21][22][23][24][25].…”

An efficient semi-analytical techniques for the fractional-order system of Drinfeld-Sokolov-Wilson equation

“…Classical derivatives have a local character, allowing us to evaluate changes in the vicinity of a point, whereas Caputo fractional derivatives have a nonlocal nature, allowing us to analyze changes in an interval. This trait makes the Caputo fractional derivative applicable to modeling a wider variety of physical phenomena, including ocean climate, atmospheric physics, dynamical systems, earthquakes, vibrations, polymers, etc (refer to the scholarly literature cited in [13][14][15][16][17][18] for additional details).…”

Study of traveling soliton and fronts phenomena in fractional Kolmogorov-Petrovskii-Piskunov equation

“…Notably, the FIM techniquebased presentation of precise solutions for these models represents a novel contribution that has not before been mentioned in the literature. The creation of soliton solutions for FPDEs is made possible by m-EDAM, an improved version of EDAM that researchers use [38,39]. In this method, a wave transformation is used to convert the FPDE into a nonlinear ODEs.…”