Abstract
In this article, we examine the unstable non-linear Shrodinger (NLS) dynamical models analytically by utilizing the tow variabke (G'/G)-expansion approach. The unstable NLS dynamical models uncover the disturbances of time evolution in the medium of marginally stable or unstable. Novel exact solutions in explicit and diverse form are constructed such as hyperbolic, exponential, trigono-metric and rational functions. Novel structures of constructed solutions of these unstable models are represented by giving suitable values to parameters. The physical constructions of few attained outcomes in various shapes such as multi-peak soliton, breather type solitary waves, bright-dark solitons etc are demonstrated graphically, which will be beneficial for realizing the complicated complex physical phenomenon of these complex models. These obtained outcomes provide the evidence of current two variable expansion scheme, which will also be helpful to solve a lot of other nonlinear physical models occurring in mathematical Physics and various other disciplines of natural sciences.