The goal of this work is to provide a novel mathematical model that explains how certain physical variables propagate (acoustic-thermal-mechanical diffusive) as waves in a photoexcited non- Gaussian laser pulse semiconductor medium. Under the impact of acoustic pressure, the isotropic and homogeneous semiconductor medium is discussed concerning the fundamental equations according to charge carrier recombination processes with optoelectronic properties. Given the impact that relaxation times have on the governing equations. Laplace transforms were utilized in a one-dimensional (1D) context to examine essential non-dimensional properties such as displacement, stress components, carrier density, temperature, and acoustic pressure in order to mathematically answer the required problem. By imposing specific initial and boundary conditions, inverse Laplace transformations were employed to generate precise solutions for the numerical modeling of different physical quantities depicted graphically. The graphical repre sentation of wave propagation data was followed by a theoretical analysis and interpretation, emphasizing the influence of other factors (such as heat rise time, relaxation times, and laser pulse effects) on the observed occurrences