Comparison between the new G'/G expansion method and the extended homogeneous balance method

In this paper, we compare the new G'/G expansion method to the extended homogeneous balance method. Both of these methods are proposed for seeking the travelling wave solutions of nonlinear partial differential equations expressed by the hyperbolic functions, trigonometric functions and rational functions. Although both of them are subjected by some modifications using the Riccati equation and the reduced nonlinear ordinary differential equation, respectively, the new G'/G expansion method is straightforward and concise, and taking special values for parameters and using some hyperbolic identities, all the solutions obtained by the extended homogeneous balance method coincide with the solutions obtained by the new G'/G expansion method. Moreover, the new G'/G expansion method gives the general form of solutions and is applied to nonlinear partial differential equations directly without using tedious calculation instead of the extended homogeneous balance method.