Muatjetjeja, B.Adem, A.R.Mbusi, Sivenathi Oscar2021-05-242021-05-242017http://hdl.handle.net/10394/37027MSc (Applied Mathematics), North-West University, Mafikeng Campus, 2017In this dissertation we study two nonlinear partial differential equations namely; the Kudryashov-Sinclshchikov equation and the Benney-Luke equation. We employ the multiplier method to find conservation laws and Kudryashov method to obtain exact solutions for the generalized Kudryashov-Sinelshchikov equation. We derive the Noether symmetries of a generalized Benney-Luke equation. Thereafter, we construct the associated conserved vectors. In addition, we search for exact solutions for the generalized Benney-Luke equation via the extended tanh method.enThesis