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Functional separation solutions of the sinh-Gordon type equations

Part of: Partial differential equations Equations and systems of special type Representations of solutions

Published online by Cambridge University Press:  26 June 2025

Giannis Polychrou Open the ORCID record for Giannis Polychrou [Opens in a new window]
Giannis Polychrou*
Affiliation:
Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
*
e-mail: ipolychr@math.auth.gr
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Abstract

In this article, 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.

Keywords

Elliptic PDEsHyperbolic PDEssinh-Gordon equationsine-Gordon equationfunctional separation

MSC classification

Primary: 35A25: Other special methods 35C05: Solutions in closed form
Secondary: 35M10: Equations of mixed type

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 68 , Issue 4 , December 2025 , pp. 1374 - 1388
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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