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

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  • Chen Peng
  • Zhao Li
  • Hongwei Zhao
  • Alessandro Formisano

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.

Suggested Citation

  • Chen Peng & Zhao Li & Hongwei Zhao & Alessandro Formisano, 2022. "New Exact Solutions to the Lakshmanan–Porsezian–Daniel Equation with Kerr Law of Nonlinearity," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-10, April.
    • Handle: RePEc:hin:jnlmpe:7340373
    DOI: 10.1155/2022/7340373
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