Communicated by S. A. MessaoudiThis paper is concerned with the generalized nonlinear Schrödinger equation with parabolic law and dual-power law. Abundant explicit and exact solutions of the generalized nonlinear Schrödinger equation with parabolic law and dualpower law are derived uniformly by using the first integral method. These exact solutions are include that of extended hyperbolic function solutions, periodic wave solutions of triangle functions type, exponential form solution, and complex hyperbolic trigonometric function solutions and so on. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial DEs.Recently, many authors have studied the dynamics of bright solitons and dark solitons that are governed by the generalized nonlinear Schrödinger equations, and some interesting results have been obtained [6,[10][11][12][13][14][15][16].In [6,10,11], some authors have studied the dynamics of bright optical solitons that are governed by the NLSE with constant and variable coefficients. In [12], the author studied dark solitons, which are known as topological optical solitons in the context of nonlinear optics. Compared with the bright soliton, which is a pulse on a zero-intensity background, the dark soliton appears as an intensity dip in an infinitely extended constant background [15]. In [16], dark solitons for a generalized nonlinear Schrödinger equation with parabolic law and dual-power law were obtained by using ansatz method.The aim of this paper is to supply a unified method for constructing a series of explicit exact solutions to the generalized nonlinear Schrödinger equation with parabolic law and dual-power law. The first integral method is employed to investigate the generalized nonlinear Schrödinger equation with parabolic law and dual-power law. Through an exhaustive analysis and discussion for different parameters, we uniformly construct a series of explicit exact solutions to Eqs. (1) and (2). Compared with ansatz method used in [10,16], the first integral method gives abundant explicit exact solitary wave solutions, periodic wave solutions of triangle function, extended hyperbolic function solutions, complex hyperbolic trigonometric function solutions, and so on. Especially, explicit exact solutions obtained in the present paper include the results obtained in [10,16] as a special case. Many known results in other previous literature are also improved and completed greatly.The rest of this paper is organized as follows. In Section 2, the outline of the first integral method will be given. In Section 3 , the method is employed to seek the explicit and exact solutions of the generalized nonlinear Schrödinger equation with parabolic law. In Section 4, the method is employed to seek the explicit and exact solutions of the generalized nonlinear Schrödinger equation with dual-power law. In the last section, some conclusion is given.We determine polynomials˛.X/,ˇ.X/, a i .X/.i D 0, 1, 2, / from Eq. (...