  This work oversees with the coupled Schr\"odinger-Boussinesq equations with
conformable derivative, which have lots of applications in laser and plasma.
The said equations are reduced to a coupled stationary form using complex
travelling wave transformation. Next Painlev\'e test applied to derived the
integrable cases of the reduced equation, after that using RCAM derived the
solution of reduced equations integrable and nonintegrable cases. Few theorems
have been presented and proved to ensure their boundedness. All presented
boundedness cases have been checked and explained by plotting the solutions for
particulars values of parameters satisfying them. The obtained solutions of
stationary form utilized to derive solutions of the coupled
Schr\"odinger-Boussinesq equations with conformable derivative. The derived
solutions have been plotted and explained. From this, it appears that these
solutions propagate by maintaining their two-hump, W-shaped, M-shaped solutions
shapes.
