The Painlevé Tests, Bäcklund Transformation and Bilinear Form for the KdV Equation with a Self-Consistent Source
The Painlevé property and Bäcklund transformation for the KdV equation with a self-consistent source are presented. By testing the equation, it is shown that the equation has the Painlevé property. In order to further prove its integrality, we give its bilinear form and construct its bilinear Bäcklu...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/872385 |
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| author | Yali Shen Fengqin Zhang Xiaomei Feng |
| author_facet | Yali Shen Fengqin Zhang Xiaomei Feng |
| author_sort | Yali Shen |
| collection | DOAJ |
| description | The Painlevé property and Bäcklund transformation for the KdV equation with a self-consistent source are presented. By testing the equation, it is shown that the equation has the Painlevé property. In order to further prove its integrality, we give its bilinear form and construct its bilinear Bäcklund transformation by the Hirota's bilinear operator. And then the soliton solution of the equation is obtained, based on the proposed bilinear form. |
| format | Article |
| id | doaj-art-d705d468c6ba46e886c0bce929f16a9e |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-d705d468c6ba46e886c0bce929f16a9e2025-02-03T01:01:12ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/872385872385The Painlevé Tests, Bäcklund Transformation and Bilinear Form for the KdV Equation with a Self-Consistent SourceYali Shen0Fengqin Zhang1Xiaomei Feng2Department of Mathematics, Yuncheng University, Yuncheng 044000, ChinaDepartment of Mathematics, Yuncheng University, Yuncheng 044000, ChinaDepartment of Mathematics, Yuncheng University, Yuncheng 044000, ChinaThe Painlevé property and Bäcklund transformation for the KdV equation with a self-consistent source are presented. By testing the equation, it is shown that the equation has the Painlevé property. In order to further prove its integrality, we give its bilinear form and construct its bilinear Bäcklund transformation by the Hirota's bilinear operator. And then the soliton solution of the equation is obtained, based on the proposed bilinear form.http://dx.doi.org/10.1155/2012/872385 |
| spellingShingle | Yali Shen Fengqin Zhang Xiaomei Feng The Painlevé Tests, Bäcklund Transformation and Bilinear Form for the KdV Equation with a Self-Consistent Source Discrete Dynamics in Nature and Society |
| title | The Painlevé Tests, Bäcklund Transformation and Bilinear Form for the KdV Equation with a Self-Consistent Source |
| title_full | The Painlevé Tests, Bäcklund Transformation and Bilinear Form for the KdV Equation with a Self-Consistent Source |
| title_fullStr | The Painlevé Tests, Bäcklund Transformation and Bilinear Form for the KdV Equation with a Self-Consistent Source |
| title_full_unstemmed | The Painlevé Tests, Bäcklund Transformation and Bilinear Form for the KdV Equation with a Self-Consistent Source |
| title_short | The Painlevé Tests, Bäcklund Transformation and Bilinear Form for the KdV Equation with a Self-Consistent Source |
| title_sort | painleve tests backlund transformation and bilinear form for the kdv equation with a self consistent source |
| url | http://dx.doi.org/10.1155/2012/872385 |
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