On Integrability of a Third-Order Complex Nonlinear Wave Equation

We show that the new third-order complex nonlinear wave equation, introduced recently by Müller-Hoissen [arXiv:2202.04512], does not pass the Painlevé test for integrability. We find two reductions of this equation, one integrable and one non-integrable, whose solutions jointly cover all solutions of the original equation.