A generalized nonlinear Schrödinger equation with logarithmic nonlinearity is studied as a model for the propagation of optical pulses. Using the ansatz method, the Gaussian solitary wave solution is derived. Numerical simulations in two- and three-dimensional postures are presented to investigate the impact of different physical parameters on the dynamics of the Gaussian solitary wave. Results show that the physical parameters of the equation play a key role in controlling the dynamics of the Gaussian solitary wave. The equation considered is: $$ i u_{t}+\alpha u_{x x}+\beta u_{x y}+\gamma u_{y y}+\lambda u\ln\left|u\right|^{2}=\kappa u+i\mu u_{x}+i\sigma u_{y}. $$ Using the ansatz $ u(x,y,t)=U(x,y,t)e^{i\Phi(x,y,t)} $, the Gaussian solitary wave is derived as: $$ u(x,y,t)=Ae^{-\left(\frac{\sqrt{2}\sqrt{(\alpha+\beta+\gamma)\lambda}}{2(\alpha+\beta+\gamma)}\right)^{2}(x+y+(2(\alpha+\beta+\gamma)+\mu+\sigma)t)^{2}}e^{i\left(-x-y-\left(2\left(\frac{\sqrt{2}\sqrt{(\alpha+\beta+\gamma)\lambda}}{2(\alpha+\beta+\gamma)}\right)^{2}(\alpha+\beta+\gamma)-\lambda\ln\left(A^{2}\right)+\kappa+\mu+\sigma+\alpha+\beta+\gamma\right)t\right)}. $$ The simulations show that increasing the dispersion coefficient $ \beta $ increases the width of the Gaussian solitary wave without changing its amplitude. Increasing the nonlinear parameter $ \lambda $ decreases the width of the wave without affecting its amplitude. Increasing the inter-modal dispersion coefficient $ \sigma $ shifts the wave to the left without changing its amplitude or width. The authors conclude that the Gaussian solitary wave solutions for this generalized nonlinear Schrödinger equation with logarithmic nonlinearity have been presented for the first time. They also mention their interest in considering high-order dispersion terms and applying other well-designed methods to other nonlinear partial differential equations.A generalized nonlinear Schrödinger equation with logarithmic nonlinearity is studied as a model for the propagation of optical pulses. Using the ansatz method, the Gaussian solitary wave solution is derived. Numerical simulations in two- and three-dimensional postures are presented to investigate the impact of different physical parameters on the dynamics of the Gaussian solitary wave. Results show that the physical parameters of the equation play a key role in controlling the dynamics of the Gaussian solitary wave. The equation considered is: $$ i u_{t}+\alpha u_{x x}+\beta u_{x y}+\gamma u_{y y}+\lambda u\ln\left|u\right|^{2}=\kappa u+i\mu u_{x}+i\sigma u_{y}. $$ Using the ansatz $ u(x,y,t)=U(x,y,t)e^{i\Phi(x,y,t)} $, the Gaussian solitary wave is derived as: $$ u(x,y,t)=Ae^{-\left(\frac{\sqrt{2}\sqrt{(\alpha+\beta+\gamma)\lambda}}{2(\alpha+\beta+\gamma)}\right)^{2}(x+y+(2(\alpha+\beta+\gamma)+\mu+\sigma)t)^{2}}e^{i\left(-x-y-\left(2\left(\frac{\sqrt{2}\sqrt{(\alpha+\beta+\gamma)\lambda}}{2(\alpha+\beta+\gamma)}\right)^{2}(\alpha+\beta+\gamma)-\lambda\ln\left(A^{2}\right)+\kappa+\mu+\sigma+\alpha+\beta+\gamma\right)t\right)}. $$ The simulations show that increasing the dispersion coefficient $ \beta $ increases the width of the Gaussian solitary wave without changing its amplitude. Increasing the nonlinear parameter $ \lambda $ decreases the width of the wave without affecting its amplitude. Increasing the inter-modal dispersion coefficient $ \sigma $ shifts the wave to the left without changing its amplitude or width. The authors conclude that the Gaussian solitary wave solutions for this generalized nonlinear Schrödinger equation with logarithmic nonlinearity have been presented for the first time. They also mention their interest in considering high-order dispersion terms and applying other well-designed methods to other nonlinear partial differential equations.