ESMA: A Local Nonlinear Schrödinger Framework with Informational Saturation and Collision Fidelity

We introduce the ESMA framework, an extension of the Schrödinger equation that incorporates locally defined nonlinear saturation mechanisms alongside a quantitative approach to wave packet interaction analysis. The model combines a logarithmic density dependent potential with a spatially localized variance operator, enabling adaptive self-confinement without reliance on global reference frames. Numerical simulations, performed using the split-step Fourier method, demonstrate regimes of suppressed dispersion, coherent propagation, and high-fidelity post collision recovery. A fidelity metric is introduced to quantify structural preservation following interactions. The results indicate that the system supports robust localized structures exhibiting soliton like behavior across a broad range of parameters. This work establishes a phenomenological framework for exploring nonlinear dynamics potentially associated with effective informational interactions.