Dispersionless BKP Equation, the Manakov–Santini System and Einstein–Weyl Structures
Abstract
We construct a map of solutions of the dispersionless BKP (dBKP) equation to solutions of the ManakovSantini (MS) system. This map defines an EinsteinWeyl structure corresponding to the dBKP equation through the general Lorentzian EinsteinWeyl structure corresponding to the MS system. We give a spectral characterisation of reduction of the MS system which singles out the image of the dBKP equation solutions 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 EinsteinWeyl structure for the BMS system.
 Publication:

Symmetry
 Pub Date:
 September 2021
 DOI:
 10.3390/sym13091699
 arXiv:
 arXiv:2108.03078
 Bibcode:
 2021Symm...13.1699B
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 General Relativity and Quantum Cosmology;
 Mathematical Physics;
 Mathematics  Differential Geometry
 EPrint:
 9 pages, LaTeX