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ON COMPUTING LINEARIZING COORDINATES FROM SYMMETRY ALGEBRA
  • +1
  • Sajid Ali,
  • Hassan Azad,
  • Waqas Shah,
  • Fazal Mahomed
Sajid Ali
Zayed University
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Hassan Azad
Abdus Salam School of Mathematical Sciences
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Waqas Shah
Abdus Salam School of Mathematical Sciences
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Fazal Mahomed
University of the Witwatersrand
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Abstract

A characterization of the symmetry algebra of the $N$th-order ordinary differential equations (ODEs) with maximal symmetry and all third-order linearizable ODEs is given. This is used to show that such an algebra $\mathfrak{g}$ determines – up to a point transformation – only one linear equation whose symmetry algebra is $\mathfrak{g}$ and an algorithmic procedure is given to find the linearizing coordinates. The procedure is illustrated by several examples from the literature.