Envelope Solitons of Nonlinear Schrodinger Equation with an Anti-cubic   Nonlinearity
  On the basis of a recently-proposed method to find solitary solutions of generalized nonlinear Schrodinger equations [1]-[3], the existence of an envelope solitonlike solutions of a nonlinear Schrodinger equation containing an anti-cubic nonlinearity (|Psi|^{-4} Psi) plus a "regular" nonlinear part is investigated. In particular, in case the regular nonlinear part consists of a sum of a cubic and a quintic nonlinearities (i.e. q_1 |Psi|^2 Psi + q_2 |Psi|^4 Psi), an upper-shifted bright envelope solitonlike solution is explicitly found. 
R. Fedele, H. Schamel, V.I. Karpman and P.K. Shukla