Stability analysis and dynamical behavior of solitons in nonlinear optics modelled by Lakshmanan–Porsezian–Daniel equation.

The current research analyses several new optical solitons solutions to the Lakshmanan–Porsezian–Daniel (LPD) equation with the Kerr law of nonlinearity which arises from the application of the Heisenberg spin chain and fiber optics, via two modified analytical methodologies. The auxiliary equation method (AE) and improved F-expansion method are used to derive several accurate solitary wave solutions of the LPD model. The key objectives of the study are in two folds. Firstly, the implementation of these schemes yields dark, bright, multi-wave, singular, alphabetic and exotic solitons solutions to the model. Secondly, we discuss the stability analysis of our selected model which confirms that the governing model is stable. For understanding the physical configuration of some constructed solitons, we plotted 2D, 3D, contours and density graphs. These solutions secured in this study will play a vital role to understand the exact dynamics of nonlinear phenomena in nonlinear optics and also enhance the previously established results. In the present era of communications network technology and nonlinear optics, the employed techniques seem to be a more categorical, influential and proficient approaches for securing optical solutions to several diversified contemporary models. [ABSTRACT FROM AUTHOR]