Functional separation solutions of the Sinh-Gordon type equations
Analysis of PDEs
2025-07-02 v4 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
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.
Cite
@article{arxiv.2310.06503,
title = {Functional separation solutions of the Sinh-Gordon type equations},
author = {G. Polychrou},
journal= {arXiv preprint arXiv:2310.06503},
year = {2025}
}