Symmetry Reductions of (2 + 1)-Dimensional CDGKS Equation and Its Reduced Lax Pairs
With the aid of symbolic computation, we obtain the symmetry transformations of the (2 + 1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation by Lou’s direct method which is based on Lax pairs. Moreover, we use the classical Lie group method to seek the symmetry groups of both the CDGKS...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/527916 |
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| author | Na Lv Xuegang Yuan Jinzhi Wang |
| author_facet | Na Lv Xuegang Yuan Jinzhi Wang |
| author_sort | Na Lv |
| collection | DOAJ |
| description | With the aid of symbolic computation, we obtain the symmetry transformations of the (2 + 1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation by Lou’s direct method which is based on Lax pairs. Moreover, we use the classical Lie group method to seek the symmetry groups of both the CDGKS equation and its Lax pair and then reduce them by the obtained symmetries. In particular, we consider the reductions of the Lax pair completely. As a result, three reduced (1 + 1)-dimensional equations with their new Lax pairs are presented and some group-invariant solutions of the equation are given. |
| format | Article |
| id | doaj-art-445c562f74d34931b3e8fde4163907e4 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-445c562f74d34931b3e8fde4163907e42025-02-03T05:51:35ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/527916527916Symmetry Reductions of (2 + 1)-Dimensional CDGKS Equation and Its Reduced Lax PairsNa Lv0Xuegang Yuan1Jinzhi Wang2School of Science, Dalian Nationalities University, Dalian 116600, ChinaSchool of Science, Dalian Nationalities University, Dalian 116600, ChinaSchool of Science, Dalian Nationalities University, Dalian 116600, ChinaWith the aid of symbolic computation, we obtain the symmetry transformations of the (2 + 1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation by Lou’s direct method which is based on Lax pairs. Moreover, we use the classical Lie group method to seek the symmetry groups of both the CDGKS equation and its Lax pair and then reduce them by the obtained symmetries. In particular, we consider the reductions of the Lax pair completely. As a result, three reduced (1 + 1)-dimensional equations with their new Lax pairs are presented and some group-invariant solutions of the equation are given.http://dx.doi.org/10.1155/2014/527916 |
| spellingShingle | Na Lv Xuegang Yuan Jinzhi Wang Symmetry Reductions of (2 + 1)-Dimensional CDGKS Equation and Its Reduced Lax Pairs Journal of Applied Mathematics |
| title | Symmetry Reductions of (2 + 1)-Dimensional CDGKS Equation and Its Reduced Lax Pairs |
| title_full | Symmetry Reductions of (2 + 1)-Dimensional CDGKS Equation and Its Reduced Lax Pairs |
| title_fullStr | Symmetry Reductions of (2 + 1)-Dimensional CDGKS Equation and Its Reduced Lax Pairs |
| title_full_unstemmed | Symmetry Reductions of (2 + 1)-Dimensional CDGKS Equation and Its Reduced Lax Pairs |
| title_short | Symmetry Reductions of (2 + 1)-Dimensional CDGKS Equation and Its Reduced Lax Pairs |
| title_sort | symmetry reductions of 2 1 dimensional cdgks equation and its reduced lax pairs |
| url | http://dx.doi.org/10.1155/2014/527916 |
| work_keys_str_mv | AT nalv symmetryreductionsof21dimensionalcdgksequationanditsreducedlaxpairs AT xuegangyuan symmetryreductionsof21dimensionalcdgksequationanditsreducedlaxpairs AT jinzhiwang symmetryreductionsof21dimensionalcdgksequationanditsreducedlaxpairs |