On the investigation of fractional coupled nonlinear integrable dynamical system: Dynamics of soliton solutions

The primary focus of this paper is the investigation of the truncated M fractional Kuralay equation, which finds applicability in various domains such as engineering, nonlinear optics, ferromagnetic materials, signal processing, and optical fibers. As a result of its capacity to elucidate a vast array of complex physical phenomena and unveil more dynamic structures of localized wave solutions, the Kuralay equation has received considerable interest in the scientific community. To extract the solutions, the recently developed integration method, referred to as the modified generalized Riccati equation mapping (mGREM) approach, is utilized as the solving tool. Multiple types of optical solitons, including mixed, dark, singular, bright-dark, bright, complex, and combined solitons, are extracted. Furthermore, solutions that are periodic, hyperbolic, and exponential are produced. To acquire a valuable understanding of the solution dynamics, the research employs numerical simulations to examine and investigate the exact soliton solutions. Graphs in both two and three dimensions are presented. The graphical representations offer significant insights into the patterns of voltage propagation within the system. The aforementioned results make a valuable addition to the current body of knowledge and lay the groundwork for future inquiries in the domain of nonlinear sciences. The efficacy of the modified GREM method in generating a wide range of traveling wave solutions for the coupled Kuralay equation is illustrated in this study.