RETRACTED ARTICLE: Wave pulses’ physical properties in birefringent optical fibres containing two vector solitons with coupled fractional LPD equation with Kerr’s law nonlinearity

In this research, the solitary wave solutions, the periodic type, and single soliton solutions are attained. The coupled fractional Lakshmanan–Porsezian–Daniel (LPD) equation is depicted the wave pulses’ physical properties in birefringent optical fibres containing two vector solitons. Here, the Paul–Painlevé operator is employed to investigate kink soliton solutions. Also, the new modified exponential Jacobi technique is used to find periodic wave and soliton, bright-dark soliton. By utilizing symbolic computation and the applied methods, the mentioned system is successfully investigated. The coupled fractional LPD model is exhibited the travelling waves, as shown by the research in the current paper. Through three-dimensional graph, contour graph, density graph, complex-plot, and two-dimensional design using Maple, the physical features of single soliton and periodic wave solutions are explained all right. The findings the investigated model’s broad variety of explicit solutions are demonstrated. As a result, the exact solitary wave solutions to the studied issues, including solitary, single soliton, and periodic wave solution are found. It is shown that the approach is practical and flexible in mathematical physics. All outcomes in this work are necessary to understand the physical meaning and behavior of the explored results and shed light on the significance of the investigation of several nonlinear wave phenomena in sciences and engineering.