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

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.

Author Biographies

Adhir Maharaj, Durban University of Technology, Steve Biko Campus, Department of Mathematics, Durban, 4000, Republic of South Africa

Senior Lecturer

Department of Mathematics

 

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

Professor

Department of Mathematics

References

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Published

2020-11-19

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