Introducing and analyzing a new combined version of the unstable Schrödinger equations with strong and weak stability effects

In the literature, two types of unstable nonlinear Schrodinger equations have been independently developed and studied. Each was derived by incorporating either a self-effect term or a time-space dispersion term into the standard nonlinear Schrodinger equation. Both models describe the time evolution of disturbances in unstable media. The primary contribution of this work is the combination of these two types into a single, new unstable version of the nonlinear Schrodinger equation. This new model is analyzed using two effective methods: the rational sine-cosine and the rational sinh-cosh functions. Additionally, a comparison test of the embedded unstable terms is conducted to assess their respective impacts on the stability of the Schrodinger model. Finally, graphical analyses, including 2D and 3D plots, are performed to validate the study’s findings.