Kerr-law nonlinearity of the resonant nonlinear Schrodinger's equation with time-dependent coefficients

This work deals with exact soliton solutions of the resonant nonlinear Schrodinger equation with time-dependent coefficients. The propagation equation that is the resonant dispersive nonlinear Schrodinger's equation with Kerr law nonlinearity is studied by two analytical methods, namely, the improved tan(phi/2)-expansion method (ITEM) and He's semi-inverse variational method (HSIVM), based upon the integration tools. 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 the HSIVM we obtained the bright soliton wave solution. Finally, by using Matlab, some graphical simulations were done to see the behavior of these solutions.