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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 05 > No. 3


On Differential Sequences

PP: 525-546
K. Andriopoulos, P.G.L. Leach, A. Maharaj,
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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