Demonstration of Sensitive Analysis and Optical Soliton Patterns in a (4+1) Dimensional Boiti-Leon-Manna Pempinelli Equation: Dynamic Insights into Bifurcation, Chaotic Behavior

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This study aims to find exact solutions for a mathematical problem known as the (4+1)-dimensional Boiti Leon Manna Pempinelli (BLMP) equation. In order to convert the governing equation into an ordinary differential equation, we make use of an appropriate wave transformation. This transformation enables the investigation of mathematical solutions, exaggerated outcomes, and normal solutions. Furthermore, in order to accurately determine the solution to this wave, we make use of the modified Khater method. We apply the given approach to find rational, the trigonometric, and hyperbolic solutions. The selected solutions provide graphic representations that accurately depict the physical behavior of the model. Using their visualization, we are able to demonstrate how their behavior changes over time in a four-dimensional space. The use of a visual representation, which involves selecting suitable values for arbitrary components, improves the understanding of the dynamical system. Furthermore, we conduct a sensitivity analysis of the dynamical system to determine the stability of the solution. The dynamical system engages in a discussion about the existence of chaotic dynamics within the Boiti Leon Manna Pempinelli equation. It is possible to depict these chaotic phenomena using two-dimensional and three-dimensional phase portraits.

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