Improved (g'/g~2)-expansion Method And Its Application

In the area of modern science, since numbers of nonlinear systems can be used to research complexity and nature of the phenomena of nature, studying these nonlinear systems becomes one of prime missions in the area of nonlinear science. However, as far as we know, nonlinear system is different from linear system because there is no standard method of the solution in the nonlinear system, which means that the method depends on the specific questions. This brought great inconvenience to its research process. Consequently, there have been a number of recent works corresponding to methods for the solution of nonlinear partial differential equations, including inverse scattcring transforma-tion, tanh function expansion method, Jacobi function expansion method, the homogeneous balance method, etc.In this paper, we further improve (g'/g2)-expansion method based on some extended and use this method for some nonlinear partial differential equations to get plenty of accurate solutions. First of all, we provide some specific processes of finding solutions of nonlinear partial differential equations using the extended (g'/g2)-expansion method. Exact solutions of generalized (2+1)-dimensional Boussinesq equation are obtained by this method; Secondly, we improve the ex-tended (g'/g2)-expansion and use this result for generalized (2+1)-dimensional Boussinesq equation to get richer exact solutions, confirming the effectiveness of such improvements; eventually, in variant Boussinesq equations as an example, illustrates the application of this method in the equations and obtains its hyper-bolic function solutions, trigonometric function solutions and rational function solutions.