Effects of fractional derivative on fiber optical solitons of (2 + 1) perturbed nonlinear Schrödinger equation using improved modified extended tanh-function method

This work explores the effect of fractional derivative on the fourth-order nonlinear Schrödinger equation with Kerr law nonlinearity, a highly significant equation in the study of wave propagation in dispersive media. By employing the improved modified extended tanh-function method, a variety of optical soliton solutions are derived. These solutions including dark solitons, bright solitons, and singular solitons. Moreover, singular periodic solutions and exponential solutions are raised. These solutions offer valuable insights into the dynamic behavior of nonlinear wave phenomena. The impact of the fractional derivative is illustrated graphically using examples of some of the retrieved solutions with various values of fractional order. Bright and dark solitons, pivotal components of our findings, play a critical role in fiber optics by facilitating the transmission of high-power optical signals with exceptional attributes such as shape preservation. These properties eliminate the need for external pulse compression, simplifying the design and operation of optical systems. The outcomes of this study contribute in advancing our knowledge of wave propagation in dispersive media and have practical implications for the development of efficient and robust optical communication technologies.