Dynamics and interaction of optical solitons in the nonlinear paraxial wave equation with sensitivity analysis

This research study explores novel multitude of optical soliton solutions of the $(2+1)$-dimensional nonlinear paraxial wave equation by three ansatzes, namely the generalised Kudryashov-auxiliary method, tan-cot method, and tanh-coth method. The model under consideration is particularly applied to the study of the wave propagation in nonlinear materials such as Kerr media. Using the simulation tool Maple, we compute breather and other optical soliton solutions in the forms of Jacobian elliptic, hyperbolic, periodic breather, breather-interaction, dark and bright solutions for the selected nonlinear paraxial wave equation with the aid of the suggested techniques. We also provide a series of two- and three-dimensional plots that represent the dynamics and interaction of the identified optical soliton solutions by assigning numerical values to the involved free parameters. We also carry out dynamical analysis to determine the stability of the model to the variation in the parameters and initial conditions and to gain a clearer understanding of how the system is prone to chaos. The obtained outcomes are very vital in fiber optics, nonlinear optics, and communication systems. Finally, the techniques used provide clear-cut soliton solutions of nonlinear partial differential equations, which can enhance the study of nonlinear wave phenomena and provide new insights into the dynamics of other complex systems.