LAUSR

In this study, the generalized $$\tan (\phi /2)$$tan(ϕ/2)-expansion method and He’s semi-inverse variational method (HSIVM) are applied to seek the exact solitary wave solutions for the resonant nonlinear Schrödinger equation with time-dependent coefficients. Using these methods, we investigate exact solutions for the nonlinear resonant Schrödinger equation with time-dependent coefficients two forms of nonlinearity, including power and dual-power law nonlinearity. Moreover, many new analytical exact solutions are obtained which are expressed by hyperbolic solutions, trigonometric solutions, and rational solutions. In addition, we obtained the bright soliton by HSIVM. These methods are powerful, efficient and those can be used as an alternative to establishing new solutions of different types of differential equations in mathematical physics and engineering.