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 (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 Schrodinger equation containing an anticubic nonlinearity (\psi\(-4) psi) 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)\psi\(2)psi + q(2)\psi\(4)psi), an upper-shifted bright envelope solitonlike solution is explicitly found.