Ultrashort laser micromachining is a versatile technology used in modern industries for manipulating transparent materials with precision. In these applications, laser systems are customized for specific power levels and wavelengths, requiring an understanding of different laser operation regimes to optimize their utilization, as well as technological advancement. This study proposes a theoretical analysis to investigate the impact of the competition between multiphoton absorption and the higher order correction term to the nonlinear refractive index on laser propagation and stability in Kerr nonlinear transparent materials. The study focuses on the mathematical model that includes a complex nonlinear K-order Ginzburg-Landau equation coupled to the Drude equation that captures the growth rate of the electron plasma density. Through global stability investigation, a diverse range of fixed points is revealed in the amplitude-frequency plane. An examination of the steady-state stability of these fixed point solutions reveals that, depending on the sign of the spatial noise, the combination of the multipho-ton absorption process with the higher-order correction term to the nonlinear refractive index can be detrimental or beneficial to the continuous-wave regime. According to numerical simulations of the mathematical model in the fully non-linear regime, we found that low values of the higher-order correction term to the nonlinear refractive index, denoted as M0 promote stable pulse trains patterns, mainly when the multiphoton absorption rate is high, whereas high values of M0 1 induced a train of anharmonic wave patterns as the multiphoton absorption rate gets stronger.