Einstein { Weyl Geometry , the dKP
نویسندگان
چکیده
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...
متن کاملEinstein–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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It is shown that Einstein–Weyl (EW) equations in 2+1 dimensions contain the dispersionless Kadomtsev–Petviashvili (dKP) equation as a special case: If an EW structure admits a constant weighted vector then it is locally given by h = dy2−4dxdt−4udt2, ν = −4uxdt, where u = u(x, y, t) satisfies the dKP equation (ut − uux)x = uyy. Linearised solutions to the dKP equation are shown to give rise to f...
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