  In this note we will fill out the details from the recent work of Fotiadis
and Daskaloyannis in arXiv:1903.05420v3, where the harmonic maps described by
Y. Shi, L. Tam and T. Y.-H. Wan (in their work Harmonic Maps on Hyperbolic
spaces with Singular Boundary Value, Differential Geometry 51(1999), 551-600)
are written by the use of Jacobi elliptic functions. We also prove that the
harmonic maps described by J. Wang in his work (The Heat Flow and Harmonic Maps
between Complete Manifolds, The Gournal of Geometric Analysis, Volume 8, Number
3, 1998, 485-514) can be written by the use of Jacobi elliptic functions, too.
