Linearization: Geometric, Complex, and Conditional
Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear (systems of) differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/303960 |
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| _version_ | 1832556149992325120 |
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| author | Asghar Qadir |
| author_facet | Asghar Qadir |
| author_sort | Asghar Qadir |
| collection | DOAJ |
| description | Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear (systems of) differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form. Not much work was done in this direction to start with, but recently there have been various developments. Here, first the original work of Lie (and the early developments on it), and then more recent developments based on geometry and complex analysis, apart from Lie’s own method of algebra (namely, Lie group theory), are reviewed. It is relevant to mention that much of the work is not linearization but uses the base of linearization. |
| format | Article |
| id | doaj-art-a2a6f628a30e4c74afd88c0138fd0558 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a2a6f628a30e4c74afd88c0138fd05582025-02-03T05:46:11ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/303960303960Linearization: Geometric, Complex, and ConditionalAsghar Qadir0Center for Advanced Mathematics and Physics, National University of Sciences and Technology, Islamabad, PakistanLie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear (systems of) differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form. Not much work was done in this direction to start with, but recently there have been various developments. Here, first the original work of Lie (and the early developments on it), and then more recent developments based on geometry and complex analysis, apart from Lie’s own method of algebra (namely, Lie group theory), are reviewed. It is relevant to mention that much of the work is not linearization but uses the base of linearization.http://dx.doi.org/10.1155/2012/303960 |
| spellingShingle | Asghar Qadir Linearization: Geometric, Complex, and Conditional Journal of Applied Mathematics |
| title | Linearization: Geometric, Complex, and Conditional |
| title_full | Linearization: Geometric, Complex, and Conditional |
| title_fullStr | Linearization: Geometric, Complex, and Conditional |
| title_full_unstemmed | Linearization: Geometric, Complex, and Conditional |
| title_short | Linearization: Geometric, Complex, and Conditional |
| title_sort | linearization geometric complex and conditional |
| url | http://dx.doi.org/10.1155/2012/303960 |
| work_keys_str_mv | AT asgharqadir linearizationgeometriccomplexandconditional |