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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/120/01/0113-0130

    • Keywords

       

      Lie symmetry; exceptional symmetries; mapping of integrals and solutions.

    • Abstract

       

      Second-and third-order scalar ordinary differential equations of maximal symmetry in the traditional sense of point, respectively contact, symmetry are examined for the mappings they produce in solutions and fundamental first integrals. The properties of the `exceptional symmetries’, i.e. those not considered to be generic to scalar equations of maximal symmetry, can be recast into a form which is applicable to all such equations of maximal symmetry. Some properties of these symmetries are demonstrated.

    • Author Affiliations

       

      P G L Leach1 R R Warne1 N Caister1 V Naicker1 N Euler2

      1. School of Mathematical Sciences, University of KwaZulu-Natal, P.O. Box X54001 Durban 4000, Republic of South Africa
      2. School of Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden

    • Dates

       
      Published
      February 2010
      Manuscript received
      2 January 2008
      Manuscript revised
      17 September 2009

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