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Mathematical Problems in Engineering
Volume 2013, Article ID 240797, 5 pages
Research Article

Conservation Laws for a Generalized Coupled Korteweg-de Vries System

International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa

Received 10 May 2013; Accepted 12 June 2013

Academic Editor: Hossein Jafari

Copyright © 2013 Daniel Mpho Nkwanazana 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.


We construct conservation laws for a generalized coupled KdV system, which is a third-order system of nonlinear partial differential equations. We employ Noether's approach to derive the conservation laws. Since the system does not have a Lagrangian, we make use of the transformation , and convert the system to a fourth-order system in , . This new system has a Lagrangian, and so the Noether approach can now be used to obtain conservation laws. Finally, the conservation laws are expressed in the , variables, and they constitute the conservation laws for the third-order generalized coupled KdV system. Some local and infinitely many nonlocal conserved quantities are found.