A recursion operator for the Kummer-Schwarz equation is determined according to the standard definition introduced by Olver (J Math Phys 18 1212-1215). Using this recursion operator and the relevent transforms we obtain the operator for the Emden-Fowler equation. The resulting sequence has interesting and excellent properties (Andriopoulos et al arXiv: 0704.3243). We examine the elements of this sequence in terms of the usual properties to be investigated – symmetries, singularity properties, integrability – 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

Username
Password