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On Differential Sequences |
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PP: 525-546 |
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Author(s) |
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K. Andriopoulos,
P.G.L. Leach,
A. Maharaj,
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Abstract |
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| We introduce the notion of Differential Sequences of ordinary differential equations.
This is motivated by related studies based on hierarchies of evolution partial differential
equations. We discuss the Riccati Sequence in terms of symmetry analysis, singularity
analysis and identification of the complete symmetry group for each member
of the Sequence. The singularity analysis reveals considerable structure for the values
of the coefficients of the leading-order terms and resonances of the different principal
branches. Full proofs of the symmetry properties are performed for differential equations
defined by their recursion properties and not given in explicit form. |
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