Abstract
In the first section of this article, we employ the parametrization of rational plane algebraic curves to characterize global solutions of certain nonlinear first-order partial differential equations of complex variables associated with rational curves. In particular, we utilize recent results that tell us that the parametrizing meromorphic functions share a common right factor. We present our main results by primarily examining examples associated with singular irreducible cubic curves. In the second section, we examine regular and entire solutions of certain quadratic second-order partial differential equations.
Acknowledgments
The authors would like to thank the referee and to thank Prof. Dimtry Khavinson and Prof. Bao Qin Li for helpful suggestions.