Einstein–weyl Spaces and Dispersionless Kadomtsev–petviashvili Equation from Painlevé I and Ii
نویسندگان
چکیده
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.
منابع مشابه
Se p 20 02 Einstein – Weyl spaces and dispersionless Kadomtsev – Petviashvili equation from Painlevé I and II .
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 cons...
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