Rational general solutions of systems of first-order algebraic partial differential equations

We study the rational solutions of systems of first-order algebraic partial differential equations and relate them to those of an associated autonomous system. We also describe how rational general solutions of these systems are related, and provide an algorithm in some particular case concerning the dimension of the associated algebraic variety. Our results can be considered as a generalization of the approach by L.  X.  C. Ngô and F. Winkler on algebraic ordinary differential equations of order one, adapted to systems of first-order algebraic partial differential equations.