The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,ux,uy)

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2012
• ISSN: 1815-0659
• Main Authors: Kuznetsova, M.N., Pekcan, A., Zhiber, A.V.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2012
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148676
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,ux,uy) / M.N. Kuznetsova, A. Pekcan, A.V. Zhiber // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 20 назв. — англ.

We present the complete classification of equations of the form uxy=f(u,ux,uy) and the Klein-Gordon equations vxy=F(v) connected with one another by differential substitutions v=φ(u,ux,uy) such that φuxφuy≠0 over the ring of complex-valued variables.