ON COMPUTING LINEARIZING COORDINATES FROM SYMMETRY ALGEBRA
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• Sajid Ali,
• Waqas Shah,
• Fazal Mahomed
Sajid Ali
Zayed University
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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.