Conservation Laws for a Generalized Coupled Korteweg-de Vries System. (8th July 2013)

• Record Type: Journal Article
• Authors: Nkwanazana, Daniel Mpho; Muatjetjeja, Ben; Khalique, Chaudry Masood
• Other Names: Jafari Hossein Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2013(2013)
• Publication Date: 2013-07-08
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2013/240797
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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 u = U x, v = V x and convert the system to a fourth-order system in U, V . 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 u, v 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.