Gaussian solitary solution for a class of logarithmic nonlinear Schrödinger equation in (1 + n) dimensions

The Gaussian solitary wave solutions are obtained for a class of logarithmic nonlinear Schrödinger equation (NLSE) with a standard harmonic oscillator potential. We find that the Gaussian solution does not exist at all in the straight line x=vt, but it does in the curve x=vt. We illustrate the behavior of the Gaussons and analyze the correlations with respect to the relevant parameters. The logarithmic nonlinearity as an imaginary term enables us to get the associated advection equation, thus showing in a novel way the existence of a Gaussian solutions in the curve x=vt. Moreover, we generalize the present study to the high-dimensional (1 + n) NLSE case. These results will enrich the current literature on this nonlinear equation.