Abstract. Further investigations of implicit solutions to nonlinear 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 are solved by the imposition of an inhomogeneous quadratic relationship among the independent variables, whose coefficients are functions of 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.

PACS number: 02.30.−f

Mathematics Subject Classification: 53C26

Print publication: Issue 20 (21 May 2004)
Received 23 January 2004, in final form 7 April 2004
Published 5 May 2004