Implicit solutions to some Lorentz invariant non-linear equations revisited
arXiv:math-ph/0412005 · doi:10.2991/jnmp.2005.12.3.8
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.
Accepted for publication in J Nonlinear Math. Phys. (Vol. 12, 2005)