Abstract
In this article, we study the unstable nonlinear Schrödinger equation (UNLSE). Analytically by modified extended direct algebraic method, which describes the disturbances in time evolution of marginally stable or unstable media. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave and elliptic function solutions of UNLSE. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomenas of this unstable equation. Moreover, we also present the formation conditions of the bright and dark solitons of UNLSE. The obtained results and computational work shows the power and effectiveness of this method. Many other such types of nonlinear evolution equations arising in engineering, applied sciences and nonlinear optics can also be solved by this method.