The usual approach on electrostatic wave decay process for a weak beam-plasma system considers two different wave modes interplaying, the Langmuir and ion-sound mode. In the present paper, a single-mode approach is shown to be feasible for conditions where the respective dispersion relations undergo topological changes. Numerical solutions for the dispersion relation of a beam-plasma system are presented, supporting the modeling of an analytic dispersion relation of a single wave mode. This wave mode is accounted for in the kinetic equations for particles and waves, which rule the evolution of the system. The results are compared against the two-wave mode approach using Langmuir and ion-sound waves, within the context of weak turbulence theory. It is found that the single-mode approach can account for the basic features of particles and waves, since the single mode exhibits both low and high frequency regions, which ultimately play the roles of ion-sound and Langmuir modes, respectively.