Different forms for exact traveling wave solutions of unstable and hyperbolic nonlinear Schrödinger equations

Abstract

In general, Schrödinger’s equations have lots of applications in quantum mechanics. Accordingly, in this paper, some new forms of the exact traveling wave solutions have been obtained for two different types of Schrödinger’s equations, namely the unstable generalized nonlinear Schrödinger’s equation and the hyperbolic nonlinear Schrödinger’s equation. In the literature one can see different forms of the solution by various existing methods. However, the applied methodology or obtained results are sometimes complicated in nature. So here to obtain the new and simple forms of the solutions for both of the equations we have used a very simple and important method known as sine-cosine method. In addition, the probability density functions (PDFs) for both of the considered problems have also been computed. To visualize the impact of the solutions, graphical representations have been made with respect to various parameters. From the results one can see, they are in terms of complex-valued functions. In special cases comparison has also been given. Furthermore, the results are computed and validated using the Maple software.