New Exact Solutions to the Lakshmanan–Porsezian–Daniel Equation with Kerr Law of Nonlinearity

Chen Peng, Zhao Li, Hongwei Zhao and Alessandro Formisano

Mathematical Problems in Engineering, 2022, vol. 2022, 1-10

Abstract: 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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:7340373

DOI: 10.1155/2022/7340373

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