Kalapet, Pondicherry - 605 014
Department of Mathematics, Pondicherry University
Tamizhmani K. M., Grammaticos B., Carstea A. S., Ramani A.
The $q$-discrete Painlevé IV equations and their properties
2004, vol. 9, no. 1, pp. 13-20
We present a detailed study of the properties of two q-discrete Painlevé IV equations: singularity structure, bilinear forms, auto-Bäcklund/Schlesinger transformations, rational solutions as well as special solutions obtained through second- or first-order linear equations.
Kruskal M. D., Tamizhmani K. M., Grammaticos B., Ramani A.
Asymmetric Discrete Painleve Equations
2000, vol. 5, no. 3, pp. 273-280
We investigate the possible integrable nonautonomous forms of a given class of mappings involving more than one dependent variable. These integrable discrete systems define "asymmetric" Painlevé equations. Our main tool of investigation is the application of the singularity confinement discrete integrability criterion. A new way of implementing it, first proposed for the singularity analysis of continuous systems, is also introduced.