INVARIANT SOLITONS AND TRAVELLING-WAVE SOLUTIONS TO A HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION IN AN OPTICAL FIBER WITH AN IMPROVED TANH-FUNCTION ALGORITHM

Optical fiber connection is essential to modern communication. A high-order nonlinear Schrödinger equation (NLSE) with additional dispersion of high-order and nonlinear components is studied in an inhomogeneous optical fiber. We provide numerous new analytic solutions via the improved modified extended tanh-function algorithm, including rational solution, singular periodic solution, Jacobi elliptic solutions (JESs), (bright, singular, dark) soliton, Weierstrass elliptic doubly periodic type solutions, and exponential solution. By employing the previously outlined method, they demonstrate their uniqueness for the given challenge. The results are presented in a clear and concise manner for various values of the necessary free parameters. Wolfram Mathematica's contour plot and 2D and 3D visualisations are used to show this process. The outcomes show how accurate, knowledgeable, and effective the computational procedures were. They may be used for increasingly complicated phenomena by integrating them with representational calculations. This finding constitutes a major advancement in our comprehension of the intricate and capricious behavior of this mathematical model.