Comparative analysis of the generalized unified method with some exact solution methods and general solutions of the Biswas–Milovic equation

Abstract

The aim of this study is twofold. First, we compare the generalized unified method (GUM), which is a new expansion method to solve nonlinear partial differential equations (NPDEs), with some methods frequently used for finding exact solutions of NPDEs. We conclude that the GUM gives more general solutions efficiently, in compact form, and with free parameters. Moreover, the algorithm of the GUM is straightforward and easy to implement on a computer. Second, as a practical example and a demonstration of effectiveness, we apply the GUM to the Biswas–Milovic equation (BME). The BME is derived from a generalized nonlinear Schrödinger equation. The BME appears in many applied fields such as the propagation of waves in nonlinear optics. We consider Kerr, power, parabolic, and dual-power-law nonlinearities of the BME. Using the GUM, we obtain the exact solution of the BME in an elegant way.