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Implicit solutions to some Lorentz invariant non-linear equations revisited

David B. Fairlie
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Abstract

An implicit solution to the vanishing of the so-called Universal Field Equation, or Bordered Hessian, which dates at least as far back as 1935 \cite{chaundy} is revived, and derived from a much later form of the solution. A linear ansatz for an implicit solution of second order partial differential equations, previously shown to have wide applicability \cite{fai} is at the heart of the Chaundy solution, and is shown to yield solutions even to the linear wave equation.

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David B. Fairlie. 2004-12-02. Implicit solutions to some Lorentz invariant non-linear equations revisited. https://doi.org/10.2991/jnmp.2005.12.3.8

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