Optical solitons to the fractional perturbed NLSE in nano-fibers

Abstract

In this paper, we study the space-time fractional perturbed nonlinear Schr \begin{document}$ \bf{\ddot o} $\end{document} dinger equation under the Kerr law nonlinearity by using the extended sinh-Gordon equation expansion method. The perturbed nonlinear Schr \begin{document}$ \bf{\ddot o} $\end{document} dinger equation is a nonlinear model which arises in nano-fibers. Some family of optical solitons and singular periodic wave solutions are successfully revealed. The parametric conditions for the existence of valid solitons are stated. Under the choice of suitable values of the parameters, the 3-dimensional and 2-dimensional graphs to some of the reported solutions are plotted.