Abstract
•W-shaped and other solitons with phases depending on the pulse intensity are derived.•The ansatz soliton solution having three different functional forms is applied.•The restrictions for the validity of optical soliton solutions are presented.•The behaviours of optical solitons are illustrated graphically.•The modulation instability by means of standard linear stability analysis is examined.
The main objective of this study is to investigate W-shaped and other types of optical solitons in nano optical fibers. The medium is described by perturbed nonlinear Schrödinger equation with Kerr law nonlinearity. The study is carried out by means of three exotic soliton ansatzes. Consequently, different forms of W-shaped solitons are derived under specific conditions. It is found that the formation of W-shaped solitons depends on the balance between the self-steepening effect and the nonlinear dispersion. Due to some restrictions, W-shaped solitons experience a decay into bright or dark solitons. Besides, numerous types of soliton solutions that describe different structures of optical solitons are extracted. These structures include bright, dark, kink-dark, kink and anti-kink solitons. The existence conditions of all optical solitons are presented. The behaviours of optical solitons are illustrated graphically by selecting suitable values for the physical parameters.