Exploring the dynamics of Lie symmetry, Bifurcation and Sensitivity analysis to the nonlinear Schrödinger model

This work focuses on examining the nonlinear Schrodinger model in 2 -dimensions which is frequently used for analyzing plasmas, coherent systems for communication and other fields of mathematical physics and engineering. Firstly, the Lie symmetries are constructed and the corresponding transformation is used to reduce the model to ordinary differential equations. Invariant solutions are established and presented through graphs. Secondly, the dynamic behavior of the model is analyzed from various approaches, including bifurcation and sensitivity analysis. Bifurcation analysis of the planar dynamical system is investigated at equilibrium points using bifurcation theory. An external periodic perturbation term is introduced in the perturbed dynamical system, which deviates from regular patterns. Sensitivity analysis is conducted at different initial conditions and the model is found to be highly sensitive. These results are novel, fascinating and theoretically useful for understanding the model. Understanding the dynamical behavior of systems and processes is crucial for making predictions and acquiring new technologies.