Optical fractals and Hump soliton structures in integrable Kuralay-Ⅱ system

The integrable Kuralay-Ⅱ system (K-IIS) plays a significant role in discovering unique complex nonlinear wave phenomena that are particularly useful in optics. This system enhances our understanding of the intricate dynamics involved in wave interactions, solitons, and nonlinear effects in optical phenomena. Using the Riccati modified extended simple equation method (RMESEM), the primary objective of this research project was to analytically find and analyze a wide range of new soliton solutions, particularly fractal soliton solutions, in trigonometric, exponential, rational, hyperbolic, and rational-hyperbolic expressions for K-IIS. Some of these solutions displayed a combination of contour, two-dimensional, and three-dimensional visualizations. This clearly demonstrates that the generated solitons solutions are fractals due to the instability produced by periodic-axial perturbation in complex solutions. In contrast, the genuine solutions, within the framework of K-IIS, take the form of hump solitons. This work demonstrates the adaptability of the K-IIS for studying intricate nonlinear phenomena in a wide range of scientific and practical disciplines. The results of this work will eventually significantly influence our comprehension and analysis of nonlinear wave dynamics in related physical systems.