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Questions about partial differential equations of hyperbolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
1
vote
Solution of a linear hyperbolic PDE
One way of tackling homogeneous equations of the form $u_{xy} + Au_x + Bu_y + Cu = 0$ is via the use of Laplace-Darboux transformations.
The technique is summarised in S.V. Meleshko Methods for Constr …
3
votes
Does there exist an electromagnetic analogue of Einstein's field equations?
A couple of suggestions:
Born-Infeld electrodynamics (Recent review article - https://arxiv.org/abs/2111.08657). The theory reduces to Maxwell's electrodynamics in the low energy limit. But it does n …