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This paper studies chirped optical solitons in nonlinear optical fibers. However, we obtain diverse soliton solutions and new chirped bright and dark solitons, trigonometric function solutions and rational solutions by adopting two formal integration methods. The obtained results take into account the different conditions set on the parameters of the nonlinear ordinary differential equation of the new extended direct algebraic equation method. These results are more general compared to Hadi et al (2018 Optik 172 545–53) and Yakada et al (2019 Optik 197 163108).

This paper uses the $\exp(-\Phi(\xi))$-Expansion method to investigate solitons to the M-fractional nonlinear Schrödingers equation with cubic nonlinearity.  The results obtained are dark solitons, trigonometric function solutions, hyperbolic solutions and rational solutions. Thus, the constraint relations between the model coefficients and the traveling wave frequency coefficient for the existence of solitons solutions are also derived.

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In this work, we are investigating a series of new optical soliton solutions to the perturbed nonlinear Schrödinger equation (PNLSE) having the form of kerr law nonlinearity with conformable space-time fractional. Thereby, two relevant integration tools known as new extended direct algebraic method and extended hyperbolic function method are applied to obtain varieties of optical soliton solutions. The series of soliton solutions with fractional derivative order obtained by these methods can be classified as complex trigonometric and hyperbolic functions as well as other elementary functions. Furthermore, conditions for validity of the obtained analytical solutions, graphical illustration (2-D, 3-D) point out the impact of the fractional-order used.

This paper studies new solitary waves for the Klein–Gordon–Zakharov equations. The obtained results are diverse and some specific ones emerge as dark, bright and bell-shape. The two integration schemes lead to obtaining waves which propagate without deformation as illustrated in graphical representations. Our obtained results are more specific compared to those obtained by Refs. 8 and 31 [C. H. Zhao and Z. M. Sheng, Acta Phys. Sin. 53 (2004) 29; S. Yakada, B. Depelair, G. Betchewe and S. Y. Doka, Optik 197 (2019) 163108].

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This paper shows out optical soliton solutions of the twin-core couplers with parabolic law nonlinearity with optical metamaterials parameters. It is used the improved new sub-ODE method (SOM) to found dark optical soliton, trigonometric function solutions, bright optical soliton and Jacobian elliptic function (JEF) solutions. Besides, physical explanation of the obtained bright and dark optical soliton solutions have been done and the influence of some parameters of the model have been set out. As the two-core coupler is favorable for modulation instability (MI), it has been studied the steady state of the results. More importantly, we have checked the effects of the optical metamaterials parameters on the formation of the Modulation bands in normal and anomalous dispersive regime. The results obtained in this paper set out Weierstrass Elliptic Function solutions compared to Mirzazadeh et al.