Group classification, optimal system and optimal reductions of a class of Klein Gordon equations

H. Azad, M. T. Mustafa, M. Ziad

Research output: Contribution to journalArticle

13 Citations (Scopus)


Complete symmetry analysis is presented for non-linear Klein Gordon equations utt = uxx + f (u). A group classification is carried out by finding f (u) that give larger symmetry algebra. One-dimensional optimal system is determined for symmetry algebras obtained through group classification. The subalgebras in one-dimensional optimal system and their conjugacy classes in the corresponding normalizers are employed to obtain, up to conjugacy, all reductions of equation by two-dimensional subalgebras. This is a new idea which improves the computational complexity involved in finding all possible reductions of a PDE of the form F (x, t, u, ux, ut, uxx, utt, uxt) = 0 to a first order ODE. Some exact solutions are also found.

Original languageEnglish
Pages (from-to)1132-1147
Number of pages16
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number5
Publication statusPublished - May 2010



  • Group classification
  • Invariant solutions
  • Lie symmetries
  • Nonlinear wave equation
  • Optimal system

ASJC Scopus subject areas

  • Applied Mathematics
  • Modelling and Simulation
  • Numerical Analysis

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