In this investigation, we have studied the application of the bifurcation theory for the Schamel Korteweg-de Vries (SKdV) equation with force term. The equation has essential repercussions in engineering and the physical sciences. Furthermore, we study the equation incorporation of stepwise forcing elements, which are necessary in seismology for modeling seismic wave propagation and geological responses to seismic events. These terms contribute to the modeling of seismic waves. We investigate the dynamical system, stability, and phase portrait analysis for the SKdV equation with force term. Furthermore, we have studied the dynamic system’s series analysis and found the system’s quasi-periodic and weak quasi-periodic behavior.