Implicit solutions of PDEs

DOI10.1088/0305-4470/37/20/009zbMATH Open1066.35027arXivmath-ph/0401034OpenAlexW1984898706MaRDI QIDQ3158663

David B. Fairlie

Publication date: 31 January 2005

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Abstract: Further investigations of implicit solutions to non-linear partial differential equations are pursued. Of particular interest are the equations which are Lorentz invariant. The question of which differential equations of second order for a single unknown $phi$ are solved by the imposition of an inhomogeneous quadratic relationship among the independent variables, whose coefficients are functions of $phi$ is discussed, and it is shown that if the discriminant of the quadratic vanishes, then an implicit solution of the so-called Universal Field Equation is obtained. The relation to the general solution is discussed.

Full work available at URL: https://arxiv.org/abs/math-ph/0401034

zbMATH Keywords

Lorentz invariantuniversal field equation

Mathematics Subject Classification ID

Subelliptic equations (35H20)

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