Asian Research Journal of Mathematics 5(1): 1-11, 2017; Article no.ARJOM.34052 ISSN: 2456-477X A Simple Model of Sediment Transport in the Nearshore Zone Evans F. Osaisai 1 ∗ 1 Department of Mathematics and Computer Sciences, Niger Delta University, PO Box 1693, Amassoma, Bayelsa State, Nigeria. Author’s contribution The sole author designed, analyzed and interpreted and prepared the manuscript. Article Information DOI: 10.9734/ARJOM/2017/34052 Editor(s): (1) Gongxian Xu, Associate Professor, Department of Mathematics, Bohai University, Jinzhou, China. Reviewers: (1) Jagdish Prakash, University of Botswana, Botswana. (2) Sumit Gandhi, Jaypee University of Engineering and Technology, Guna, India. (3) Rajkumar V. Raikar, KLE Dr. M. S. Sheshgiri College of Engineering and Technology, India. Complete Peer review History: http://www.sciencedomain.org/review-history/19865 Received: 11 th May 2017 Accepted: 12 th June 2017 Original Research Article Published: 4 th July 2017 Abstract In this paper we examine a simple model of sediment transport, induced by the breaking waves in the surf zone. Essentially the bottom is allowed to move in response to the divergence of a sediment flux, in turn determined by the breaking waves. The effect of this extra term on the previous solutions for set-up, longshore currents and rip currents is then determined. It is found that the solutions for the mean flow are now unsteady on a slow timescale determined by a certain sediment transport parameter. There is a change in beach slope in the rip currents controlled by the sediment transport. The system of equations now forms a three-by-three nonlinear hyperbolic system of equations. These we solve approximately, using a simple wave solution based on the simple wave speed corresponding to the small sediment transport parameter. However, this solution will always breakdown after a long time, so we show that by adding another term proportional to the beach slope into the expression for the sediment flux, we can obtain a steady-state solution. *Corresponding author: E-mail: fevansosaisai@gmail.com;