Closed-form solutions of some partial differential equations, via quasi- solutions. I (Q1813017)

New explicit solutions are found for some partial differential equations, including the Klein-Gordon, p-eikonal, and minimal surface equations. The method is to find so-called quasi-solutions of a given equation P. They are functions v that are functions of actual solutions u. They are shown to be actual solutions of a higher-order system \(P^*\). From the quasi- solutions, the original actual solutions can be recovered. Symbolic computation on computers is used to do the heavy-duty calculations. [For part II, see the following review.]