Dark solitons for a combined potential KdV and Schwarzian KdV equations with t-dependent coefficients and forcing term

In this work we formally derive the dark soliton solutions for the combined potential KdV and Schwarzian KdV equations. The combined KdV and Schwarzian KdV equations with time-dependent coefficients and forcing term are then investigated to obtain dark soliton solutions. The solitary wave ansatz is used to carry out the analysis for both models.