<p>In recent years, research on generalized wave equations has garnered significant attention. By incorporating additional characteristic scale parameters of medium and high-order spatial derivatives of state variables, these equations effectively characterize the perturbational effects of complex microstructures on seismic wave propagation, offering a novel paradigm for high-fidelity wavefield modeling. To advance imaging and inversion applications of generalized wave equations, it is essential to investigate multi-mode and multi-component wavefield propagation characteristics, where wavefield decoupling and separation emerge as pivotal techniques. Accurately and efficiently extracting P- and S-wave components can directly enhance wavefield mechanism analysis and imaging quality. This approach eliminates crosstalk noise induced by wave-mode coupling, thereby enhancing imaging precision and physical interpretability. This study addresses the equation decoupling-based method for wavefield separation in generalized wave equations, conducting comprehensive numerical tests and analyses to validate the efficacy. Results demonstrate that the proposed equation decoupling-based algorithm preserves full wavefield integrity while accurately maintaining amplitude and phase fidelity, establishing a robust data foundation for high-precision seismic imaging, inversion and interpretation.</p>