Gaussian solitary waves for argument-Schrödinger equation

Abstract We present localized analytical solutions of the logarithmic nonlinear Schrodinger equation, i.e., the so-called the argument-Schrodinger equation. The Gaussian solitary waveform is shown to be the solution, and we obtain the explicit form in a one-dimensional case when the dynamics evolve under a quadratic potential. The dispersion relation becomes time-dependent due to the logarithmic nonlinearity.