Exploring the Variable Base Soliton Solutions and Stability Analysis for a Nonlinear Model With Dual-Power Nonlinearity

This work studies variable-coefficient soliton outcomes for the nonlinear model with dual-power nonlinearity, which is significant for explaining the superconductivity of steady ion-cyclotron waves in nonhomogeneous plasma and drift cyclotron waves. The enhanced modified simple equation approach is used to construct variable-coefficient soliton solutions for the proposed model. First, the traveling-wave transformation with time-dependent frequency and wave speed is applied to change the proposed model into an ordinary differential form. Then, we solve it through the enhanced modified simple equation approach. The findings are demonstrated here in exponential, trigonometric, and hyperbolic form. For the wave speed, like tant,sect,sinht,tanht,secht,tn,e±t, the obtained solutions are presented as solitons. The complex phenomena are presented through 3D and 2D plots. Finally, the stability analysis also studied the proposed model to explain how small changes in field amplitude give rise to solitary structures, domain walls, and vortices. A stability study of the proposed model shows how nonlinear interactions influence wave evolution and establishes stability constraints in optical, quantum, and cosmic environments. From the above analysis, the applied method is more effective in offering more complex phenomena.