On some canonical classes of cubic-quintic nonlinear Schrodinger equations

In this paper we bring into attention variable coefficient cubic-quintic nonlinear Schrodinger equations which admit Lie symmetry algebras of dimension four. Within this family, we obtain the reductions of canonical equations of nonequivalent classes to ordinary differential equations using tools of Lie theory. Painleve integrability of these reduced equations is investigated. Exact solutions through truncated Painleve expansions are achieved in some cases. One of these solutions, a conformal-group invariant one, exhibits blow-up behavior in finite time in L-p, L-infinity norm and in distributional sense. (C) 2016 Elsevier Inc. All rights reserved.