Optical soliton solutions of the unstable nonlinear Schrödinger equation

The Unstable Nonlinear Schrödinger Equation (UNLSE) is fundamental for understanding optical fibre light pulse propagation. The unstable form explains modulated wave train instabilities and disturbance propagation in stable and unstable mediums. The Complete Discriminant System for Polynomials Method will analyse UNLSE non-linear dynamics. We use computational libraries like Axes3D, mpl toolkits.mplot3d, numpy and pandas, scipy.fftpack, and matplotlib.pyplot as plt to create time series, 2-dimensional and 3-dimensional plots, Poincaré maps, and various optical soliton solutions, including trigonometric, Jacobi elliptic, hyperbolic, periodic waves, singular solitary waves solutions, and rational soliton waves solutions. Additionally, stability analyses are performed and illustrated visually to confirm the converging constraints of appropriate parameters.