Cotton-Type and Joint Invariants for Linear Elliptic Systems. (25th December 2013)

• Record Type: Journal Article
• Authors: Aslam, A.; Mahomed, F. M.
• Other Names: Baleanu D. Academic Editor.; Jafari H. Academic Editor.; Khalique C. M. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2013(2013)
• Publication Date: 2013-12-25
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2013/540705
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : Cotton-type invariants for a subclass of a system of two linear elliptic equations, obtainable from a complex base linear elliptic equation, are derived both by spliting of the corresponding complex Cotton invariants of the base complex equation and from the Laplace-type invariants of the system of linear hyperbolic equations equivalent to the system of linear elliptic equations via linear complex transformations of the independent variables. It is shown that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results.