Modulation of localized solutions for the Schrödinger equation with logarithm nonlinearity

• We investigate localized solutions of the logarithm Schrödinger equation.
• Similarity transformation converts the equation into an autonomous form.
• The stability of such solutions is investigated numerically.

We investigate the presence of localized analytical solutions of the Schrödinger equation with logarithm nonlinearity. After including inhomogeneities in the linear and nonlinear coefficients, we use similarity transformation to convert the nonautonomous nonlinear equation into an autonomous one, which we solve analytically. In particular, we study stability of the analytical solutions numerically.