Bäcklund Transformations for Integrable Geometric Curve Flows
We study the Bäcklund transformations of integrable geometric curve flows in certain geometries. These curve flows include the KdV and Camassa-Holm flows in the two-dimensional centro-equiaffine geometry, the mKdV and modified Camassa-Holm flows in the two-dimensional Euclidean geometry, the Schrödi...
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MDPI AG
2015-08-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/7/3/1376 |
| _version_ | 1811308023422910464 |
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| author | Changzheng Qu Jingwei Han Jing Kang |
| author_facet | Changzheng Qu Jingwei Han Jing Kang |
| author_sort | Changzheng Qu |
| collection | DOAJ |
| description | We study the Bäcklund transformations of integrable geometric curve flows in certain geometries. These curve flows include the KdV and Camassa-Holm flows in the two-dimensional centro-equiaffine geometry, the mKdV and modified Camassa-Holm flows in the two-dimensional Euclidean geometry, the Schrödinger and extended Harry-Dym flows in the three-dimensional Euclidean geometry and the Sawada-Kotera flow in the affine geometry, etc. Using the fact that two different curves in a given geometry are governed by the same integrable equation, we obtain Bäcklund transformations relating to these two integrable geometric flows. Some special solutions of the integrable systems are used to obtain the explicit Bäcklund transformations. |
| first_indexed | 2024-04-13T09:14:33Z |
| format | Article |
| id | doaj.art-92e4ac05dbd8401091cf76b727aa1449 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T09:14:33Z |
| publishDate | 2015-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-92e4ac05dbd8401091cf76b727aa14492022-12-22T02:52:46ZengMDPI AGSymmetry2073-89942015-08-01731376139410.3390/sym7031376sym7031376Bäcklund Transformations for Integrable Geometric Curve FlowsChangzheng Qu0Jingwei Han1Jing Kang2Department of Mathematics, Ningbo University, Ningbo 315211, ChinaSchool of Information Engineering, Hangzhou Dianzi University, Hangzhou 310018, ChinaDepartment of Mathematics, Northwest University, Xi\'an 710069, ChinaWe study the Bäcklund transformations of integrable geometric curve flows in certain geometries. These curve flows include the KdV and Camassa-Holm flows in the two-dimensional centro-equiaffine geometry, the mKdV and modified Camassa-Holm flows in the two-dimensional Euclidean geometry, the Schrödinger and extended Harry-Dym flows in the three-dimensional Euclidean geometry and the Sawada-Kotera flow in the affine geometry, etc. Using the fact that two different curves in a given geometry are governed by the same integrable equation, we obtain Bäcklund transformations relating to these two integrable geometric flows. Some special solutions of the integrable systems are used to obtain the explicit Bäcklund transformations.http://www.mdpi.com/2073-8994/7/3/1376invariant geometric flowBäcklund transformationintegrable systemdifferential invariant |
| spellingShingle | Changzheng Qu Jingwei Han Jing Kang Bäcklund Transformations for Integrable Geometric Curve Flows Symmetry invariant geometric flow Bäcklund transformation integrable system differential invariant |
| title | Bäcklund Transformations for Integrable Geometric Curve Flows |
| title_full | Bäcklund Transformations for Integrable Geometric Curve Flows |
| title_fullStr | Bäcklund Transformations for Integrable Geometric Curve Flows |
| title_full_unstemmed | Bäcklund Transformations for Integrable Geometric Curve Flows |
| title_short | Bäcklund Transformations for Integrable Geometric Curve Flows |
| title_sort | backlund transformations for integrable geometric curve flows |
| topic | invariant geometric flow Bäcklund transformation integrable system differential invariant |
| url | http://www.mdpi.com/2073-8994/7/3/1376 |
| work_keys_str_mv | AT changzhengqu backlundtransformationsforintegrablegeometriccurveflows AT jingweihan backlundtransformationsforintegrablegeometriccurveflows AT jingkang backlundtransformationsforintegrablegeometriccurveflows |