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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:2111.09759 (nlin)
[Submitted on 18 Nov 2021]

Title:The quadric ansatz for the $mn$-dispersionless KP equation, and supersymmetric Einstein-Weyl spaces

Authors:Maciej Dunajski, Prim Plansangkate
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Abstract:We consider two multi-dimensional generalisations of the dispersionless Kadomtsev-Petviashvili (dKP) equation, both allowing for arbitrary dimensionality, and non-linearity. For one of these generalisations, we characterise all solutions which are constant on a central quadric. The quadric ansatz leads to a second order ODE which is equivalent to Painleve I or II for the dKP equation, but fails to pass the Painlevé test in higher dimensions. The second generalisation of the dKP equation leads to a class of Einstein-Weyl structures in an arbitrary dimension, which is characterised by the existence of a weighted parallel vector field, together with further holonomy reduction. We construct and characterise an explicit new family of Einstein-Weyl spaces belonging to this class, and depending on one arbitrary function of one variable.
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Differential Geometry (math.DG)
Cite as: arXiv:2111.09759 [nlin.SI]
  (or arXiv:2111.09759v1 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.2111.09759
Related DOI: https://doi.org/10.1088/1751-8121/ac5160

Submission history

From: Maciej Dunajski [view email]
[v1] Thu, 18 Nov 2021 15:39:39 UTC (16 KB)
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