5 papers
High Lewis number combustion wavefronts: a perturbative Melnikov analysis
S. Balasuriya, G. A. Gottwald, J. Hornibrook +1
The wavefronts associated with a one-dimensional combustion model with Arrhenius kinetics and no heat loss are analyzed within the high Lewis number perturbative limit. This situat…
Blending two discrete integrability criteria: singularity confinement and algebraic entropy
S. Lafortune, A. Ramani, B. Grammaticos +2
We confront two integrability criteria for rational mappings. The first is the singularity confinement based on the requirement that every singularity, spontaneously appearing duri…
Linearisable systems and the Gambier approach
S. Lafortune, B. Grammaticos, A. Ramani
A systematic study of the discrete second order projective system is presented, complemented by the integrability analysis of the associated multilinear mapping. Moreover, we show…
A Study of the Continuous and Discrete Gambier Systems
A. Ramani, B. Grammaticos, S. Lafortune
We present a systematic study of the Gambier system, which in the continuous case is given by two Riccati equations in cascade. We derive the condition for its integrability and sh…
Schlesinger Transformations for Linearisable Equations
A. Ramani, B. Grammaticos, S. Lafortune
We introduce the Schlesinger transformations of the Gambier equation. The latter can be written, in both the continuous and discrete cases, as a system of two coupled Riccati equat…