Cotton-Type and Joint Invariants for Linear Elliptic Systems
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...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/540705 |
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| _version_ | 1832559783321796608 |
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| author | A. Aslam F. M. Mahomed |
| author_facet | A. Aslam F. M. Mahomed |
| author_sort | A. Aslam |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a9cf0f4d07124e368ec6cc67368e988f |
| institution | Kabale University |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-a9cf0f4d07124e368ec6cc67368e988f2025-02-03T01:29:17ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/540705540705Cotton-Type and Joint Invariants for Linear Elliptic SystemsA. Aslam0F. M. Mahomed1Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, South AfricaDifferential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, South AfricaCotton-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.http://dx.doi.org/10.1155/2013/540705 |
| spellingShingle | A. Aslam F. M. Mahomed Cotton-Type and Joint Invariants for Linear Elliptic Systems The Scientific World Journal |
| title | Cotton-Type and Joint Invariants for Linear Elliptic Systems |
| title_full | Cotton-Type and Joint Invariants for Linear Elliptic Systems |
| title_fullStr | Cotton-Type and Joint Invariants for Linear Elliptic Systems |
| title_full_unstemmed | Cotton-Type and Joint Invariants for Linear Elliptic Systems |
| title_short | Cotton-Type and Joint Invariants for Linear Elliptic Systems |
| title_sort | cotton type and joint invariants for linear elliptic systems |
| url | http://dx.doi.org/10.1155/2013/540705 |
| work_keys_str_mv | AT aaslam cottontypeandjointinvariantsforlinearellipticsystems AT fmmahomed cottontypeandjointinvariantsforlinearellipticsystems |