Obliquely propagating optical wave patterns to the (2 + 1)-dimensional chiral nonlinear Schrödinger equation in the absence and presence of Atangana derivative

The study aims to explore obliquely propagating optical wave solutions to the (2 + 1)-dimensional chiral nonlinear Schrödinger (NLS) equation in both the absence and presence of the Atangana derivative. In order to convert the classical-order chiral nonlinear Schrödinger equation to an ordinary differential equation, a transformation associated with wave obliqueness is applied. Hereafter, the unified method is applied to the reduced equation. As outcomes, the dark, periodic singular with unequal wave length, periodic with equal wavelength, periodic, unsmooth periodic, singular periodic soliton solutions are received to the ordinary differential equation. Later, the acquired solutions are then put to the applied transformation associated with obliqueness. Moreover, the fractional-order chiral NLS equation is solved by using the spatiotemporal Atangana derivative with oblique wave transformation and the unified method. In terms of wave obliqueness, fractionality, and applied technique sense, all generated wave solutions are revealed to be novel. Along with their physical explanations, the impacts of obliqueness and fractionality on the solutions are graphically illustrated. It is exposed that as obliqueness and fractionality increase, the optical wave phenomena change. Additionally, it is discovered that the employed method can be used to obtain novel optical soliton features to the chiral nonlinear Schrödinger equation with or without fractional and obliqueness constraints. It can be assured that the utilized method is more powerful than the other methods. As a result, the method can be used in future research to explain the many physical phenomena that arise in optical fiber communication networks.