Explicit solutions of nonlinear wave equation systems

We apply the (G'/G)-expansion method to solve two systems of nonlinear differential equation and construct traveling wave solutions expressed in terms of hyperbolic functions, trigonometric functions, and rational functions with arbitrary parameters. We highlight the power of the (G'/G)-expansion method in providing generalized solitary wave solutions of different physical structures. It is shown that (G'/G)-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear differential equation systems in mathematical physics.