In this study, some new exact travelling wave solutions to the Lakshmanan–Porsezian–Daniel (LPD) equation with Kerr law of nonlinearity are retrieved by the complete discrimination system for the polynomial method. Under the travelling wave transformation, the LPD equation is reduced to an ordinary differential equation. The new exact travelling wave solutions including rational solutions, triangle function solutions, solitary wave solutions, and Jacobian elliptic function solutions are obtained and graphically illustrated using three-dimensional and two-dimensional graphs. Comparing with the previous results for LPD equation, some of new solutions in this work such as elliptical solution are not studied, which shows the complete discrimination system method is efficient.
In this paper, the coupled Kundu-Mukherjee-Naskar (KMN) model in Bragg grating fibers is considered to retrieve some new optical soliton solutions in (
2
+
1
) dimensions. Plenty of new exact solutions, including rational function solutions and triangle function solutions, in addition to the Jacobian elliptic function solutions, are obtained by using a complete discrimination system method. The 3D-surface plots, 2D-shape plots, and corresponding 2D contour plots of some obtained solutions are drawn, which provides a visualized structures and propagation of solitons. The novel results are new and show the effectiveness of the proposed method.
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