Extracting novel categories of analytical wave solutions to a nonlinear Schrödinger equation of unstable type

Solving partial differential equations has always been one of the significant tools in mathematics for modeling applied phenomena. In this paper, using an efficient analytical technique, exact solutions for the unstable Schrödinger equation are constructed. This type of the Schrödinger equation describes the disturbance of time period in slightly stable and unstable media and manages the instabilities of lossless symmetric two stream plasma and two layer baroclinic. The basis of this method is the generalization of some commonly used methods in the literature. To better demonstrate the results, we perform many numerical simulations corresponding to the solutions. All these solutions are new achievements for this form of the equation that have not been acquired in previous research. As one of the strengths of the article, it can be pointed out that not only is the method very straightforward, but also can be used without the common computational complexities observed in known analytical methods. In addition, during the use of the method, an analytical solution is obtained in terms of familiar elementary functions, which will make their use in practical applications very convenient. On the other hand, the utilized methodology empowers us to handle other types of well-known models. All numerical results and simulations in this article have been obtained using computational packages in Wolfram Mathematica. •Abundant analytical solutions to the Schrodinger equation of unstable type are obtained.•We perform several numerical simulations related to the achieved results.•An efficient logarithmic transformation is employed to integrate the equation.•The effects of two existing parameters in the model are also examined.