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Einstein--Weyl spaces and dispersionless Kadomtsev--Petviashvili equation from Painlevé I and II | | Maciej Dunajski
; Paul Tod
; | | Date: |
17 Apr 2002 | | Journal: | Phys.Lett. A303 (2002) 253-264 | | Subject: | Exactly Solvable and Integrable Systems; Differential Geometry | nlin.SI gr-qc math.DG | | Abstract: | We present two constructions of new solutions to the dispersionless KP (dKP) equation arising from the first two Painlevé transcendents. The first construction is a hodograph transformation based on Einstein--Weyl geometry, the generalised Nahm’s equation and the isomonodromy problem. The second construction, motivated by the first, is a direct characterisation of solutions to dKP which are constant on a central quadric. We show how the solutions to the dKP equations can be used to construct some three-dimensional Einstein--Weyl structures, and four--dimensional anti-self-dual null-Kähler metrics. | | Source: | arXiv, nlin.SI/0204043 | | Services: | Forum | Review | PDF | Favorites | |
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