PROPERTIES OF A DIFFERENTIAL SEQUENCE BASED UPON THE KUMMER-SCHWARZ EQUATION
DOI:
https://doi.org/10.14311/AP.2020.60.0428Keywords:
lie symmetries, singularity analysis, differential sequenceAbstract
In this paper, we determine a recursion operator for the Kummer-Schwarz equation, which leads to a sequence with unacceptable singularity properties. A different sequence is devised based upon the relationship between the Kummer-Schwarz equation and the first-order Riccati equation for which a particular generator has been found to give interesting and excellent properties. We examine the elements of this sequence in terms of the usual properties to be investigated – symmetries, singularity properties, integrability, alternate sequence – and provide an explanation of the curious relationship between the results of the singularity analysis and a consideration of the solution of each element obtained by quadratures.
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Copyright (c) 2020 Adhir Maharaj, Kostis Andriopoulos, Peter Leach
This work is licensed under a Creative Commons Attribution 4.0 International License.