Various exact solutions for two special type RKL models

In this paper, the higher order nonlinear Schrödinger equation with cubic–quintic nonlinear terms in non-Kerr media, which presented by Radhakrishnan, Kundu and Laskshmanan (RKL model for short), are researched. With the aid of the elliptic-like subsidiary ordinary differential equation (sub-ODE for short) and the sine–cosine method, the various exact solutions of two special type RKL models are derived provided that the coefficients of two special type RKL models satisfy certain constraint conditions. The exact solutions and the constraint conditions are very helpful for the optical engineering.