Envelope solitons of nonlinear schrödinger equation with an anti-cubic nonlinearity

On the basis of a recently-proposed method to find solitary solutions of generalized nonlinear Schrödinger equations (Fedele R and Schamel H 2002 Eur. Phys. J. B 27 313, Fedele R 2002 Phys. Scr. 65 502, Fedele R, Schamel H and Shukla P K 2002 Phys. Scr. T 98 18), the existence of envelope solitonlike solutions of a nonlinear Schrödinger equation containing an anti-cubic nonlinearity (|ψ|-4ψ) plus a 'regular' nonlinear part is investigated. In particular, in the case that the regular nonlinear part consists of a sum of cubic and quintic nonlinearities (i.e. q 1|ψ|2ψ + q2|ψ|4ψ), an upper-shifted bright envelope solitonlike solution is explicitly found