Analyzing the decoupled nonlinear Schrödinger equation: fractional optical wave patterns in the dual-core fibers

This paper investigate the dynamic behavior of decoupled nonlinear Schr & ouml;dinger equation describing the propagation of optical pulses in dual-core optical fibers. The integrable coupled system is discussed with the effect of group-velocity dispersion and group-velocity mismatch, linear coupling coefficient and nonlinear refractive index as well as the truncated M-fractional derivative. The governing system is transformed into the coupled ordinary differential equations by the assistance of the fractional complex wave transformation. Moreover, a variety of optical pulses in the forms of bright, dark, singular, combined as well as the hyperbolic, periodic and exponential function solutions have been secured by applying the recently introduced techniques namely, the generalized Arnous method and the multivariate generalized exponential rational integral function approach. Notably, in comparison with the existing approaches, it is obvious that the proposed methods are the straightforward, efficient and practical way to handle various nonlinear models appearing in applied sciences and provide a variety of soliton solutions. The results described in this work are able to enhance the nonlinear dynamical behavior of a given system and confirm the effectiveness of the methods used. In order to clarify the physical meaning and scientific interpretation of the analytical work, the obtained solutions are plotted in different graphs of some appropriate parameter values. Our results provide valuable insights into the complexity of nonlinear equations, improving previous results in the field by introducing novel methods and revealing a large number of solutions with broad applicability.