arXiv subjects

G. Polychrou

Publications and source records attributed to G. Polychrou.

2 recordsLinked to original sources

arXiv2023

Functional separation solutions of the Sinh-Gordon type equations

In this paper, we address the following question: Which hyperbolic or elliptic PDEs admit functional separable solutions. We shall focus on the study of a sinh-Gordon type equation. We construct solutions to this equation via the method of functional separation. We prove that these are the only families that have the property of functional separation and so we obtain a classification. To this end, we construct new families of solutions for the hyperbolic and elliptic versions of both sine and sinh Gordon equations in a unified way.

math.AP↗

arXiv2020

A Note on harmonic maps

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.

math.DG↗