Stability, modulation instability and traveling wave solutions of (3+1)dimensional Schrödinger model in physics

The nonlinear Schr & ouml;dinger equation is one of the most important physical model in optical fiber theory for comprehension of the fluctuations of optical bullet development. In this study, the exact bullet solutions for the (3+1)-dimensional Schr & ouml;dinger equation which demonstrate the bullet behaviours in optical fibers can be accumulated through the Sardar sub-equation method and the unified method. The applied strategies may retrieve several kinds of optical bullet solutions within one frameworks as well as is quite simple and reliable. Mathematica are utilised for describing the dynamics of different wave structures as 3D, 2D, and contour visualisations for a given set of parameters. As a result, we are able to develop a variety of travelling wave structures namely the periodic, singular and V shaped soliton wave solutions. The stability analysis for the derived results is analysed efficiently while the modulation instability for the governing model has also been studied to demonstrate the reliability of the research. The approaches implemented here works perfectly and can be extended to deal with many advanced models in contemporary areas of science and engineering. The solutions attain by using these techniques are robust, unique and straight forward and has applications in different fields of physics, engineering and mathematical science. Specially physical applications of these obtain results are in the transmission of data in optical fibers. We also add the graphics for the better understanding of the attain solutions behaviour.