Optical soliton solutions and modulation instability for unstable conformable Schrödinger model

The unstable time fractional Schrödinger model (UTFSM) is studied through the development of disturbances in marginally stable or unstable media. A modified Sardar-sub equation technique (MSSE) for a conformable fractional-order nonlinear evolution model is presented in this paper. The objective here is to construct new wave solutions for UTFSM. These solutions have particular relevance in quantum physics and assume several forms such as rational, exponential, trigonometric and hyperbolic functions, as well as combo solutions. This technique produces various shapes of dark, kink-type solitons and periodic solitary waves by setting proper parametric values. These discrete physical frameworks contribute to an understanding from analysis of unstable dynamical models. Additionally, we investigate modulation instability and stability analysis to ensure that obtained solutions are highly stable. The multiplicity of waves and solutions emphasizes how this technique can be used for different nonlinear fractional models in quantum physics and other areas.