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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).

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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.

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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The telecommunications revolution finds its foundation thanks to new service offerings including voice, images, security of computer data and much more. Thereby, telecommunications can be defined as the transmission of information at a distance using electronic, computer, wired, optical or electromagnetic technologies. At an expense of these characteristics, this paper explores the dynamics of various travelingwaves, through telecommunications systems. In this perspective, we use a ([Formula: see text])-dimensional nonlinear transmission line equation, by solving it analytically using a novel developed techniques: The improved Sardar-subequation. As a result, we discover several novel voltage characteristics such as bright, trigonometric, exponential and dark function solutions. Using certain appropriate values, we provide several different surfaces of the solutions produced in this work. These findings will be essential in the telecommunications system used to represent wave propagations.