Abstract
This study examines the generalized nonlinear Schrödinger equation for the propagation of femtosecond pulses in highly-nonlinear optical medium with polynomial Kerr nonlinearity and arbitrary higher-order non-Kerr components. The polynomial complete discriminant system is used to obtain exact solutions and chirped soliton solutions of complete types of nonlinear Schrödinger equation. Exact solutions can be of three types: soliton solutions, singular solutions, and elliptic function double periodic solutions. The model is also visualized under specific parameter values, and the classical two-dimensional diagrams of exact solutions and chirped soliton solutions are given to prove the existence of solutions.
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