A variable coefficient nonlinear Schrödinger equation with a four-dimensional symmetry group and blow-up

A canonical variable coefficient nonlinear Schrödinger equation with a four-dimensional symmetry group containing SL(2, ℝ) group as a subgroup is considered. This typical invariance is then used to transform by a symmetry transformation a known solution that can be derived by truncating its Painlevé expansion and study blow-ups of these solutions in the L _p-norm for p > 2, L _∞-norm and in the sense of distributions.