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

A canonical variable coefficient nonlinear Schrödinger equation with a four dimensional symmetry group containing $\SL(2,\mathbb{R})$ 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 $p>2$, $L_\infty$-norm and in the sense of distributions.