Article

Nonlinear Dynamics

, Volume 30, Issue 2, pp 167-177

Nonclassical Potential Symmetry Generators of Differential Equations

  • A. G. JohnpillaiAffiliated withSchool of Mathematics, Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand
  • , A. H. KaraAffiliated withSchool of Mathematics, Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand

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Abstract

We determine the nonclassical potential symmetries for a number ofequations that arise in the literature. A large number of these areobtained for some equations which only admit a single potential(classical) symmetry (e.g., the wave equation and the motion of wavesthrough some medium). However, we show that some of the exact solutionsinvariant under the nonclassical potential symmetries are equivalent toknown solutions but these solutions are not obtainable through theclassical point or potential symmetries. The Korteweg–deVries equation,it is shown, does not admit nonclassical potential symmetries – as inthe classical case.

nonclassical potential symmetries