In this paper we obtain the stationary solutions of various nonlinear Schrödinger equations. We use Lie symmetry method to find the stationary solutions of the Gerdjikov-Ivanov equation, cubic-quintic and paraxial nonlinear Schrödinger equations.

The Kundu–Mukherjee–Naskar model is studied to reveal some vital optical solitons in (2[Formula: see text]+[Formula: see text]1) dimensions. To obtain singular soliton, dark soliton, combined dark-singular soliton and other hyperbolic solutions, we will use csch method, extended Tanh–Coth method and extended rational sinh-cosh method receptively with constraint conditions.

This paper retrieves chirped sub-pico optical pulses for Triki–Biswas equation with the help of two integration architectonics. This model discusses ultrashort pulses propagation in optical fiber in the presence of non-Kerr dispersion term and group velocity dispersion. We will obtain bright, dark and dark singular combo-optical solitons under some constraint conditions.