Abundant soliton solutions of the resonant nonlinear Schrödinger equation with time-dependent coefficients by ITEM and He’s semi-inverse method

Abstract

The improved $$\tan (\phi /2)$$ -expansion method (ITEM) and He’s semi-inverse variational method (HSIVM) are the efficient methods for obtaining exact solutions of nonlinear differential equations. In this paper, the ITEM and HSIVM are applied to construct exact solutions of the resonant nonlinear Schrodinger equation (RNLSE) with time-dependent coefficients for parabolic law nonlinearity. The resonant nonlinear Schrodinger equation plays a very important role in mathematical physics and nonlinear optics. We compare analytical findings with the results of the other analytical schemes describing the ansatz method approach and expansion method are used to carry out the integration. Description of the ITEM is given and the obtained results reveal that the ITEM is a new significant method for exploring nonlinear partial differential models. Moreover, by help of the HSIVM we obtained the bright and dark soliton wave solutions. Finally, by using Matlab, some graphical simulations were drawn to see the behavior of these solutions.