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The main consideration of this paper is to discuss cubic optical solitons in a polarization-preserving fiber modeled by nonlinear Schrödinger equation (NLSE). We extract the solutions in the forms of hyperbolic, trigonometric including a class of solitary wave solutions like dark, bright–dark, singular, singular periodic, multiple-optical soliton and mixed complex soliton solutions. A recently developed integration tool known as new extended direct algebraic method (NEDAM) is applied to analyze the governing model. Moreover, the studied equation is discussed with two types of nonlinearity. The constraint conditions are explicitly presented for the resulting solutions. The accomplished results show that the applied computational system is direct, productive, reliable and can be carried out in more complicated phenomena. [ABSTRACT FROM AUTHOR]

In this research, a particular attention has been given on the fractional Fokas-Lenells equation via Atangana-Baleanu derivative operator that describe the propagation of short pulses in optical fibers. The integrability properties has been investigated while using the modified Khater method that we present in details. As a result, number of new soliton solutions are obtained along with constraints on some parameters that are introduced accordingly. For further details about our obtained solutions, some distinct types of solutions have been illustrated to explain more physical and dynamical behavior of the short wave pulses in the optical fibers. [ABSTRACT FROM AUTHOR]