In this work, the methodology of the exp(-Phi(xi)) method is given. The effectiveness of the method is demonstrated by applications to two nonlinear partial differential equations (NPDEs), namely, the Zakharov Kuznetsov-Benjamin Bona Mahony (ZK-BBM) equation and ill-posed Boussinesq equation. The obtained exact solutions are consist of trigonometric, hyperbolic and rational functions. (C) 2016 Elsevier GmbH. All rights reserved.