Optical soliton and other solutions to the nonlinear dynamical system via two efficient analytical mathematical schemes

This article will discuss the (2+1)-dimensional nonlinear dynamical conformable generalized Schrodinger system to represent the optical pulse propagation in monomode optical fibers. Optical soliton solutions of the given equations will be found using novel tools, namely the new extended hyperbolic function method and the Sine-Gordon equation expansion method. The suggested methods will extract various solutions such as optical bright, dark, singular, periodic, combined bright-drak, and mixed singular soliton solutions. The derived solutions are explained using contour graphs, 3-dimensional surface graphs, and 2-dimensional line profiles to visualize the theoretical outcomes. The dynamics of exact explicit solutions of nonlinear dynamical systems play a crucial role in the theory of solitons and the formations of exact analytical solutions perform an important role in the area of nonlinear sciences and applied mathematics. Moreover, these analytical solutions may ensure dynamical and physical behavior of the system which assist us about the mechanism of considered complex nonlinear systems. This work allows the reader to get a better understanding of the various techniques that have been disputed. The obtained findings reveal that the procedures we have adopted are straightforward, powerful, effective, and precise to implement and that they apply to a wide range of more challenging issues.