Abstract
The purpose of this paper is to study the optical soliton solutions of nonlinear Schrödinger equation with quintic non-Kerr nonlinear term describing the nonlinear wave state of optical solitons, which is a noteworthy and important model in optical fiber communication. By using the polynomial complete discrimination system, the various optical soliton solutions of the nonlinear Schrödinger equation are obtained including the trigonometric function solution, the hyperbolic function solution and the Jacobian elliptic function solution. Finally, the graphs of some obtained solutions are drawn by setting values to the parameters.
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