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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 278672, 10 pages
http://dx.doi.org/10.1155/2014/278672
Research Article

Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg-de Vries Equation

1Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou, Jiangsu 221008, China
2Department of Chemical Engineering, University of Chemical Technology and Metallurgy, Sofia, 8 Kliment Ohridsky Boulevard, 1756 Sofia, Bulgaria
3Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3R4
4Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 15 May 2014; Accepted 29 May 2014; Published 12 June 2014

Academic Editor: Dumitru Baleanu

Copyright © 2014 Xiao-Jun Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A mathematical model of fractal waves on shallow water surfaces is developed by using the concepts of local fractional calculus. The derivations of linear and nonlinear local fractional versions of the Korteweg-de Vries equation describing fractal waves on shallow water surfaces are obtained.