Optical soliton solutions for Lakshmanan-Porsezian-Daniel equation with parabolic law nonlinearity by trial function method

Chen Peng; Zhao Li; Chen Peng; Zhao Li

doi:10.3934/math.2023138

AIMS Mathematics

2023, Volume 8, Issue 2: 2648-2658. doi: 10.3934/math.2023138

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Research article

Optical soliton solutions for Lakshmanan-Porsezian-Daniel equation with parabolic law nonlinearity by trial function method

Chen Peng ^{1,2
,
,},
Zhao Li ¹

1.
College of Computer Science, Chengdu University, Chengdu 610106, China
2.
V. C. & V. R. Key Lab of Sichuan Province, Sichuan Normal University, Chengdu 610068, China

Received: 17 September 2022 Revised: 13 October 2022 Accepted: 25 October 2022 Published: 08 November 2022
MSC : 35C05, 35C07, 35R11

In this paper, the trial function method is used to address the Lakshmanan-Porsezian-Daniel (LPD) equation with parabolic law nonlinearity. Implementing the traveling wave hypothesis reduces the LPD equation to an ordinary differential equation (ODE). From this ODE, many exact solutions, such as kink solitary wave solutions, bell shaped solitary wave solutions, triangular function solutions, periodic function solutions, singular solutions and Jacobian elliptic function solutions, are retrieved. Among them, some solutions are new. By suitable choice of parameters, we also draw 3D surface and 2D graphs of density, contour and level curves of some precise solutions for intuitive investigation.
- solitons,
- trial function method,
- Lakshmanan-Porsezian-Daniel equation
Citation: Chen Peng, Zhao Li. Optical soliton solutions for Lakshmanan-Porsezian-Daniel equation with parabolic law nonlinearity by trial function method[J]. AIMS Mathematics, 2023, 8(2): 2648-2658. doi: 10.3934/math.2023138

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Abstract

In this paper, the trial function method is used to address the Lakshmanan-Porsezian-Daniel (LPD) equation with parabolic law nonlinearity. Implementing the traveling wave hypothesis reduces the LPD equation to an ordinary differential equation (ODE). From this ODE, many exact solutions, such as kink solitary wave solutions, bell shaped solitary wave solutions, triangular function solutions, periodic function solutions, singular solutions and Jacobian elliptic function solutions, are retrieved. Among them, some solutions are new. By suitable choice of parameters, we also draw 3D surface and 2D graphs of density, contour and level curves of some precise solutions for intuitive investigation.

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