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


KUZNETSOVA M. N. , Pekcan A., ZHIBER A. V.

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, vol.8, 2012 (Peer-Reviewed Journal) identifier identifier

  • 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, Scopus

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.