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Keywords = the dispersionless BKP hierarchy

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8 pages, 221 KiB  
Article
Dispersionless BKP Equation, the Manakov–Santini System and Einstein–Weyl Structures
by Leonid V. Bogdanov
Symmetry 2021, 13(9), 1699; https://doi.org/10.3390/sym13091699 - 15 Sep 2021
Cited by 1 | Viewed by 2020
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Symmetry of Hamiltonian Systems: Classical and Quantum Aspects)
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