Analytical soliton solutions for cubic-quartic perturbations of the Lakshmanan-Porsezian-Daniel equation using the modified extended tanh function method

Abstract

In this paper, the improved modified extended Tanh function technique is used to find analytical solutions to the cubic-quartic Lakshmanan-Porsezian-Daniel model which describes the pulse propagation in optical fiber. Using the traveling wave theory, the nonlinear partial differential form of the cubic-quartic Lakshmanan-Porsezian-Daniel equation is transformed into an ordinary differential equation. Then applying the proposed methods bright, dark, bright-dark, periodic, singular, and Jacobian elliptic solutions were derived as analytical solutions. Besides, hyperbolic, rational, trigonometric, and exponential functions were also obtained. In order to understand the obtained solutions, graphical simulations were depicted by 3D surfaces and 2D graphs.

Keywords

• Nonlinear Schrödinger equation
• Improved modified extended tanh–function method
• Auxiliary equation
• Optical solitons
• Analytical solutions
• Travelling waves structures