Exact solutions to the resonant nonlinear Schrödinger equation with time-dependent coefficients under dual-power law nonlinearity

In this paper, the resonant nonlinear Schr & ouml;dinger equation with time-dependent coefficients which appears in the research process of Madelung fluid is probed by means of two different methods. As an outcome, dozens of distinct types of complex exact solutions are built in the condition of taking dual-power law nonlinearity into account. More specifically, a range of complex solitary, soliton as well as elliptic wave solutions are offered in terms of the unified method, and a series of hyperbolic, triangular, Jacobi elliptic doubly periodic, rational as well as exponential type solutions are given in the light of the improved modified extended tanh-function method. Moreover, the dual-power law nonlinearity, it should be noted, can degenerate to other popular nonlinearity forms including the kerr, power, parabolic law nonlinearities and quadratic-cubic nonlinearity with specific values of concerned parameters, and we also consider these peculiar circumstances in the solving process. Finally, we draw 2D, 3D and contour images for distinct types of solutions that we acquired to simplify the physical interpretation.