Soliton solutions of fractional modified unstable Schrödinger equation using Exp-function method

Abstract

An efficient technique, namely Exp-function method is used to construct the new exact analytic solutions of universal problem fractional modified unstable Schrödinger equation (FMUSE) with varying dispersion, nonlinearity, and the gain or absorption which could describe the propagation of optical pulse in inhomogeneous fiber systems. As a result, we secure exact solutions in the forms of hyperbolic, rational as well as soliton like solutions. The constrained conditions which ensure the existence of the solutions are also listed. A generalized fractional wave transformation is properly used for the conversion of this equation into an ordinary differential equation (ODE). Moreover, we also sketch 3D, 2D, contour, and 3D-implicit plots of some attained solutions by appropriate selection of parameters to clarify and visualize the physical features of the problem. These solutions are to be attractive to researchers for understanding the complexity of the considered model. The results reconfirm the worth and effectiveness of the used method. Moreover, the presented method is powerful and can be used to solve many other unstable nonlinear problems of mathematical physics.