<p>This paper proposes a novel staged training Fourier feature physics-informed neural networks (FF-PINNs) method, which effectively captures the details of high-frequency information. By integrating multiple training strategies and employing stage optimization, the proposed method enhances the convergence and stability of the model, thereby improving its capability to address complex physical phenomena. The method has been successfully applied to the precise prediction of soliton dynamics in the cubic-quintic nonlinear Schrödinger equation. Comparative analysis with traditional PINNs and FF-PINNs reveals that this method significantly reduces gradient oscillations during the optimization process and improves computational efficiency and robustness. It also exhibits substantial superiority over conventional methods in terms of both computational efficiency and prediction accuracy. It offers a novel and practical tool for studying high-order nonlinear system dynamics, with potential applications in nonlinear optics, fluid dynamics, quantum mechanics, and other fields requiring accurate modeling of complex wave phenomena.</p>