Solitary and periodic wave solutions of the unstable nonlinear Schrödinger’s equation

Abstract

Solving partial differential equations has always been one of the significant mathematical tools for modeling applied phenomena in various fields. In this paper, our main motivation is to find the traveling wave solutions of unstable nonlinear Schrödinger equation (UNLSE) which describes the two layer baroclinic instability, and two lossless symmetric stream plasma instability, and also disturbance of time period in both stable and unstable media. The methods which are used to endure these solutions are extended rational sine-cosine/sinh-cosh. New solutions are constructed in the different forms such as hyperbolic and trigonometric. The achieved results present that proposed techniques are consequential for exploring several types of nonlinear partial differential equations (NLPDEs) in applied sciences and solutions are presented in the form of novel periodic, dark, bright, and periodically bright solitons. These methods are highly effective, robust, and provide an alternative approach for establishing new soliton solutions for various types of partial differential equations (PDEs) used in mathematical physics.