IJPAM: Volume 42, No. 3 (2008)
THE CONNECTION TO DIFFERENTIAL SEQUENCES
Centre for Research and Applications of Nonlinear Systems
Department of Mathematics
University of Patras
Patras, GR-26500, GREECE
and
School of Mathematical Sciences
University of KwaZulu-Natal
Durban, 4041, REPUBLIC OF SOUTH AFRICA
e-mail: kand@aegean.gr
Abstract.In ordinary differential equations differential sequences are the analogues of the hierarchies found for partial differential equations such as the KdV hierarchy. We initiate our study by considering the generalised symmetries of the potential Burgers' equation and show how these lead naturally to the Riccati sequence, the first two members of which are the Riccati equation and the Painlevé-Ince equation. The properties of both the Riccati and Emden-Fowler sequences are intriguing and the generalised Riccati sequence gives some insight to the uniqueness associated with the former.
Received: August 17, 2007
AMS Subject Classification: 34M55, 47E05
Key Words and Phrases: differential sequences, Lie symmetries, singularity analysis, hierarchies
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 42
Issue: 3
