Application of Painlevé analysis to the wave-wave scattering problem in a two-level resonant medium

In this paper, we apply the Painlevé singularity structure analysis to the wave-wave scattering problem which manifests itself in nonlinear optics as the stimulated Raman scattering (SRS) and self-induced transparency (SIT) and in plasma physics as the interaction of electromagnetic waves with the ion-acoustic waves. The governing equations are expected to be integrable from the point of view of Painlevé (P) analysis.