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

• Main Authors: Adhir Maharaj, Kostis Andriopoulos, Peter Leach
• Format: Article
• Language: English
• Published: CTU Central Library 2020-11-01
• Series: Acta Polytechnica
• Subjects: lie symmetries; singularity analysis; differential sequence
• Online Access: https://ojs.cvut.cz/ojs/index.php/ap/article/view/6103

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.