On the Solutions of a Fifth Order Nonlinear Partial Differential Equation of Fluids

This paper studies a fifth order nonlinear partial differential equation that describes nonlinear waves in fluids and oceans. Exact solutions are obtained for this equation using the travelling wave variable. This transforms the nonlinear partial differential equation into a nonlinear ordinary differential equation. Thereafter, by invoking the Kudryashov's method and the simplest equation method we seek exact solutions. The solutions gained are the travelling wave solutions. Finally, the dynamics of the obtained solutions are displayed in 3D and 2D graphs.