On the study of multiple wave profiles and hybrid phenomena to the newly developed multi-component Gross-Pitaevskii system and stability analysis - Muhammad Bilal; Shafqat Ur Rehman; Yazen M. Alawaideh; Ioan-Lucian Popa; Bashar M. Al-khamiseh (Ain Shams Engineering Journal, 2025)
This research investigates a dynamical analysis of the newly developed Gross-Pitaevskii equations, focusing on finding exact soliton solutions. By uncovering these solutions, this research aims to understand the complicated dynamics underlying superfluidity, superconductivity, and associated nonlinear phenomena, thereby providing valuable insights into the behavior of these systems. The considered model is analytically examined using advanced integration tools, such as the new extended hyperbolic function and Kumar-Malik methods. Diverse wave solutions are extracted in hyperbolic, periodic, Jacobi elliptic, exponential functions, and complex multiple soliton structures. We meticulously simulate and verify all reported solutions using the Wolfram Mathematica package. The achieved outcomes have significant implications for several scientific disciplines, spanning optical fiber, plasma physics, mathematical physics, condensed matter physics, and fluid dynamics. Additionally, we display different wave profiles with the appropriate parametric values and plot the gain spectrum for the modulation instability analysis. This visualization strategy increases our comprehension of the derived solutions and expedites an in-depth exploration of their potential real-world applications. The aforementioned techniques provide a robust foundation for examining the nonlinear phenomena encountered in numerous physical domains. The key novelty of this study lies in its pioneering application of two effective analytical methods to a previously unexplored model, thereby filling a significant knowledge gap in the field.