The Klein-Gordon Equation and Differential Substitutions of the Form v = phi(u, u(x), u(y))

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Kuznetsova M. N., Pekcan A., Zhiber A. V.

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, vol.8, 2012 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 8
• Publication Date: 2012
• Doi Number: 10.3842/sigma.2012.090
• Journal Name: SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Istanbul University Affiliated: Yes

Abstract

We present the complete classification of equations of the form u(xy) = f(u, u(x,) u(y)) and the Klein-Gordon equations v(xy) = F (v) connected with one another by differential substitutions v = phi(u, u(x,) u(y)) such that phi(ux)phi(uy) not equal 0 over the ring of complex-valued variables.