A variable coefficient nonlinear Schr\"{o}dinger equation with a   four-dimensional symmetry group and blow-up of its solutions
  A canonical variable coefficient nonlinear Schr\"{o}dinger 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 Painlev\'e 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. 
F. G\"ung\"or, M. Hasanov and C. \"Ozemir
math.AP nlin.SI