In this article, we employ the nonlinear complex Hirota-dynamical model which is one of the famous and important standards to the nonlinear Schrödinger equation in which the third derivative term represent the self-interaction in the high-frequency subsystem. Specially, in plasma this term is isomorphic to the so known self-focusing effect. The bright, dark and periodic optical soliton solutions to this equation will realized successfully for the first time in the framework of the solitary wave ansatz method. Furthermore, in this connection at the same time and parallel the extended simple equation method has been applied successfully to achieve new impressive solitary wave solutions to this model. A comparison between the obtained results and that satisfied in previous work has been established.
This paper is about the study of space-time fractional Fokas-Lenells equation that describes nonlinear wave propagation in optical fibers. Three prominent schemes are employed for extracting different types of exact soliton solutions. In particular, the expa function method, the hyperbolic function method and the simplest Riccati equation scheme are investigated for the said model. As a sequela, a series of soliton solutions are obtained and verified through Mathematica. The obtained solutions are significant additions in some specific fields of physics and engineering. Furthermore, the 3D graphical descriptions are left to analyze the pulse propagation for the reader.