Abstract
In this paper, we use the extended trial equation method (ETEM) to construct the exact solutions in many different functions such as the trigonometric function, elliptic integral function, rational function, hyperbolic function and Jacobi elliptic functions for nonlinear evolution equation in mathematical physics via the fifth-order modified nonlinear Kawahara equation. In this method, the balance number is not constant as we have shown in other methods, but it is changed by changing the trial equation derivative definition. This method is powerful, reliable, effective and simple for solving more complicated nonlinear partial differential equations in mathematical physics.