Dynamics of solitons and modulation instability in a (2+1)-dimensional coupled nonlinear Schrödinger equation

This study uses the complex amplitude ansatz and semi-inverse methods to explore the closed-form exact optical soliton solutions of a (2+1)-dimensional coupled nonlinear Schrödinger (NLS) equation. Delving into the specified methods unveils the enigmatic dynamic presence of solitons within the solutions of the NLS equation. These methods produce specific possible solutions of the equation that contain enough free physical parameters. Also, the phase shift and intensity of the soliton solutions are presented. The results of produced solutions are reported as bright, anti-bright, dark, kink, anti-kink, stationary, and one-solitons. This study explores soliton solution of the NLS equation not known earlier. Furthermore, we performed a comprehensive modulation instability (MI) analysis using linear standard stability analysis, providing valuable insights into this phenomenon. Graphical representations of the solutions such as two-dimensional (2D), three-dimensional (3D), and contour plots have been illustrated with appropriate parameter values to provide additional insight into these innovative solutions. It is found that MI gain and instability bandwidth can be controlled by the equations parameter, initial incidence power and perturbation wave numbers.