This paper investigates a generalized nonlinear Schrödinger (gNLS) equation with logarithmic nonlinearity as a model for the propagation of optical pulses. The authors use the ansatz method to derive the Gaussian solitary wave solution of the governing equation. Numerical simulations in two- and three-dimensional spaces are conducted to examine the impact of different physical parameters on the dynamics of the Gaussian solitary wave. The results show that the dispersion coefficient \(\beta\), the nonlinear parameter \(\lambda\), and the inter-modal dispersion coefficient \(\sigma\) significantly influence the wave's width and position. Specifically, increasing \(\beta\) increases the wave's width without changing its amplitude, enhancing \(\lambda\) decreases the wave's width without affecting its amplitude, and increasing \(\sigma\) shifts the wave to the left without changing its amplitude or width. The study provides valuable insights into the behavior of optical pulses in media with logarithmic nonlinearity.This paper investigates a generalized nonlinear Schrödinger (gNLS) equation with logarithmic nonlinearity as a model for the propagation of optical pulses. The authors use the ansatz method to derive the Gaussian solitary wave solution of the governing equation. Numerical simulations in two- and three-dimensional spaces are conducted to examine the impact of different physical parameters on the dynamics of the Gaussian solitary wave. The results show that the dispersion coefficient \(\beta\), the nonlinear parameter \(\lambda\), and the inter-modal dispersion coefficient \(\sigma\) significantly influence the wave's width and position. Specifically, increasing \(\beta\) increases the wave's width without changing its amplitude, enhancing \(\lambda\) decreases the wave's width without affecting its amplitude, and increasing \(\sigma\) shifts the wave to the left without changing its amplitude or width. The study provides valuable insights into the behavior of optical pulses in media with logarithmic nonlinearity.