Error analysis of a first-order IMEX scheme for the logarithmic Schrödinger equation

Lilian Wang, Jingye Yan, Xiaolong Zhang

The logarithmic Schrödinger equation (LogSE) has a logarithmic nonlinearity $f(u)=u\ln |u{|}^2$ that is not differentiable at $u=0.$ Compared with its counterpart with a regular nonl…