Closed-form solutions of some partial differential equations, via quasi- solutions. II (Q1813018)

[For part I, cf. the preceding review.] All solutions u of the form \(u=\phi (A(x)+B(y))\) of Laplace's equation \(u_{xx}+u_{yy}=0\) in two variables are found. The proof is very computational. Besides the obvious solutions, there are some new ones involving integrals of Jacobi's elliptic functions. Corresponding results are found for the wave equation and the heat equation. The case of three and more independent variables is also discussed.