To investigate the effects of inlet pressure perturbations on the propagation characteristics of rotating detonation waves (RDWs), numerical simulations were conducted using the OpenFOAM platform and the two-dimensional Euler equations coupled with detailed chemical kinetics. A two-dimensional unfolded rotating detonation combustor model was established to represent the annular chamber. Periodic boundary conditions were applied in the circumferential direction, and non-reflecting boundary conditions were imposed at the outlet. Discretized premixed injection units were specified at the inlet to simulate the reactant supply process. High-frequency, small-amplitude pressure perturbations with a frequency of 5 kHz and an amplitude of 0.1 MPa were superimposed on the inlet total pressure with a mean value of 1 MPa, while the inlet total temperature was fixed at 300 K. Hydrogen–air mixtures with equivalence ratios ranging from 0.6 to 1.6 were considered to examine the influence of reactant composition on RDW behavior under perturbed inlet conditions. The governing equations were solved using a density-based compressible reacting-flow solver with a finite-volume discretization scheme. Convective fluxes were calculated using the KNP central-upwind scheme with a van Leer limiter, and time integration was performed using a second-order Crank-Nicolson method. A detailed hydrogen–air chemical reaction mechanism consisting of 27 elementary reactions was employed to capture detonation dynamics. The results indicate that the RDW wavenumber and propagation mode exhibit significant responses to inlet pressure perturbations at different equivalence ratios, which are mainly governed by the dual-wave collision process and the reactant replenishment characteristics ahead of the detonation front. The combustor adaptively balances the energy release and stable RDW propagation, allowing the system to stabilize at different wavenumbers through a nonlinear dynamic equilibrium. Under inlet pressure perturbations, flow parameters and RDW characteristics exhibit periodic responses at the perturbation frequency, with the RDW structure being more sensitive to the perturbations. The equivalence ratio and RDW propagation mode jointly determine the combustion heat release level and the outlet thrust, whereas the specific impulse is primarily controlled by the equivalence ratio and shows a weak correlation with the RDW wavenumber. High-frequency, small-amplitude inlet pressure perturbations mainly affect the wave structure and propagation mode of RDWs, while the mean performance parameters are only weakly influenced.