A novel model for lasing cavities in the presence of population inversion: Bifurcation and stability analysis

•A model for laser cavities in an external field, in the presence of population inversion PI.•Exact solutions of the A Model for lasing Cavities in the Presence of Population Inversion.•The homogeneous equilibrium states HESs are determined and the bifurcation against the relevant parameters is analyzed qualitatively. Very recently a discrete model for laser cavities in an external field, in the presence of population inversion PI, was developed. Here, a model where attention is focused to a discrete PI, with gain or loss, is presented. The continuum model is constructed. The behavior of the field intensity and the PI is investigated. This is done by obtaining the exact solutions of the model equation by using the unified method. We think that this main objective of this work, which we think that it is completely new. The homogeneous equilibrium states HESs are determined and the bifurcation against the relevant parameters is analyzed qualitatively. Further the stability analysis of the HESs against in homogeneous perturbation near these states, is studied quantitatively, via solving the eigenvalue problems. It is shown that the wave intensity and the PI shows set on of giant pulses formation (or Q-swithing). Which depends on pulse duration, pulse energy, frequency and pumping rate. High power laser pulses are observed. The pulse duration is estimated. It is shown that the holding beam amplitude, the dispersion coefficient and the carrier pumping rate play significant roles on the number of the emitted photons.