Dispersionless BKP Equation, the Manakov–Santini System and Einstein–Weyl Structures
We construct a map from solutions of the dispersionless BKP (dBKP) equation to solutions of the Manakov–Santini (MS) system. This map defines an Einstein–Weyl structure corresponding to the dBKP equation through the general Lorentzian Einstein–Weyl structure corresponding to the MS system. We give a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/9/1699 |
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| author | Leonid V. Bogdanov |
| author_facet | Leonid V. Bogdanov |
| author_sort | Leonid V. Bogdanov |
| collection | DOAJ |
| description | We construct a map from solutions of the dispersionless BKP (dBKP) equation to solutions of the Manakov–Santini (MS) system. This map defines an Einstein–Weyl structure corresponding to the dBKP equation through the general Lorentzian Einstein–Weyl structure corresponding to the MS system. We give a spectral characterisation of reduction in the MS system, which singles out the image of the dBKP equation solution, and also consider more general reductions of this class. We define the BMS system and extend the map defined above to the map (Miura transformation) of solutions of the BMS system to solutions of the MS system, thus obtaining an Einstein–Weyl structure for the BMS system. |
| first_indexed | 2024-03-10T07:10:27Z |
| format | Article |
| id | doaj.art-40f4fadd270c4d238f3016831dd9621e |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T07:10:27Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-40f4fadd270c4d238f3016831dd9621e2023-11-22T15:28:41ZengMDPI AGSymmetry2073-89942021-09-01139169910.3390/sym13091699Dispersionless BKP Equation, the Manakov–Santini System and Einstein–Weyl StructuresLeonid V. Bogdanov0Landau Institute for Theoretical Physics RAS, 142432 Chernogolovka, RussiaWe construct a map from solutions of the dispersionless BKP (dBKP) equation to solutions of the Manakov–Santini (MS) system. This map defines an Einstein–Weyl structure corresponding to the dBKP equation through the general Lorentzian Einstein–Weyl structure corresponding to the MS system. We give a spectral characterisation of reduction in the MS system, which singles out the image of the dBKP equation solution, and also consider more general reductions of this class. We define the BMS system and extend the map defined above to the map (Miura transformation) of solutions of the BMS system to solutions of the MS system, thus obtaining an Einstein–Weyl structure for the BMS system.https://www.mdpi.com/2073-8994/13/9/1699dispersionless integrable systemsthe Manakov–Santini systemEinstein–Weyl structuresthe dispersionless BKP hierarchy |
| spellingShingle | Leonid V. Bogdanov Dispersionless BKP Equation, the Manakov–Santini System and Einstein–Weyl Structures Symmetry dispersionless integrable systems the Manakov–Santini system Einstein–Weyl structures the dispersionless BKP hierarchy |
| title | Dispersionless BKP Equation, the Manakov–Santini System and Einstein–Weyl Structures |
| title_full | Dispersionless BKP Equation, the Manakov–Santini System and Einstein–Weyl Structures |
| title_fullStr | Dispersionless BKP Equation, the Manakov–Santini System and Einstein–Weyl Structures |
| title_full_unstemmed | Dispersionless BKP Equation, the Manakov–Santini System and Einstein–Weyl Structures |
| title_short | Dispersionless BKP Equation, the Manakov–Santini System and Einstein–Weyl Structures |
| title_sort | dispersionless bkp equation the manakov santini system and einstein weyl structures |
| topic | dispersionless integrable systems the Manakov–Santini system Einstein–Weyl structures the dispersionless BKP hierarchy |
| url | https://www.mdpi.com/2073-8994/13/9/1699 |
| work_keys_str_mv | AT leonidvbogdanov dispersionlessbkpequationthemanakovsantinisystemandeinsteinweylstructures |