PROPERTIES OF A DIFFERENTIAL SEQUENCE BASED UPON THE KUMMER-SCHWARZ EQUATION

Adhir Maharaj; Kostis Andriopoulos; Peter Leach

doi:10.14311/AP.2020.60.0428

Authors

Adhir Maharaj Durban University of Technology, Steve Biko Campus, Department of Mathematics, Durban, 4000, Republic of South Africa
Kostis Andriopoulos University of KwaZulu-Natal, School of Mathematical Sciences, Private Bag X54001, Durban,4000, Republic of South Africa
Peter Leach Durban University of Technology, Steve Biko Campus, Department of Mathematics, Durban, 4000, Republic of South Africa; University of KwaZulu-Natal, School of Mathematical Sciences, Private Bag X54001, Durban,4000, Republic of South Africa

DOI:

https://doi.org/10.14311/AP.2020.60.0428

Keywords:

lie symmetries, singularity analysis, differential sequence

Abstract

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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