Bifurcation analysis and phase portraits for chiral solitons with bohm potential in quantum hall effect.

This paper presents a comprehensive bifurcation analysis and phase portrait investigation of chiral solitons governed by the chiral nonlinear Schrödinger equation with Bohm potential in the Quantum Hall Effect framework. The equation accounts for chirality, quantum corrections, and nonlinear interactions, making it a valuable model for soliton behavior in quantum fluids. We analyze the system's dynamical properties, equilibrium points, and solution regimes using bifurcation theory, revealing stability transitions and structural changes in soliton solutions. Phase plane techniques visualize qualitative behaviors under varying parameters. Additionally, we derive exact optical soliton solutions, demonstrating the Bohm potential's influence on soliton formation and evolution. These findings offer insights into nonlinear wave propagation in chiral quantum systems and have potential applications in condensed matter physics and optical fiber systems. The paper analyzes chiral solitons using bifurcation theory and phase portraits to reveal stability transitions and dynamic behaviors. Exact soliton solutions are derived, highlighting the effects of Bohm potential and chirality on soliton formation. The results provide insights into nonlinear wave propagation in quantum fluids and optical fiber systems.