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- F W Nijhoff, A Ramani, Y Ohta
- 1998

1 Abstract A new integrable nonautonomous nonlinear ordinary difference equation is presented which can be considered to be a discrete analogue of the Painlevé V equation. Its derivation is based on the similarity reduction on the two-dimensional lattice of integrable partial difference equations of KdV type. The new equation which is referred to as GDP… (More)

- A Ramani, B Grammaticos, Paris, France K M Tamizhmani, S Lafortune, France
- 1998

We examine a family of 3-point mappings that include mappings solvable through lin-earization. The different origins of mappings of this type are examined: projective equations and Gambier systems. The integrable cases are obtained through the application of the singularity confinement criterion and are explicitly integrated.

- A Ramani, S Lafortune, Paris, France
- 1998

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 equations in cascade involving an integer parameter n. In the continuous case the parameter appears explicitly in the equation while in the discrete case it corresponds to the number… (More)

- A Ramani, S Lafortune, Paris, France Y Ohta
- 2001

We examine a family of discrete second-order systems which are integrable through reduction to a linear system. These systems were previously identified using the singularity confinement criterion. Here we analyse them using the more stringent criterion of nonex-ponential growth of the degrees of the iterates. We show that the linearisable mappings are… (More)

We confront two integrability criteria for rational mappings. The first is the singularity confinement based on the requirement that every singu-larity, spontaneously appearing during the iteration of a mapping, disappear after some steps. The second recently proposed is the algebraic entropy criterion associated to the growth of the degree of the iterates.… (More)

With the growing popularity of wireless technology in the healthcare area, there is a pressing need to have a proper system in place for patient identification. Errors in patient identification and hence improper administration of medication for example can lead to disastrous results. Also an efficient algorithm needs to be in place to allocate patients to… (More)

- A Ramani, S Tremblay
- 2008

We examine whether the Painlevé property is a necessary condition for the integra-bility of nonlinear ordinary differential equations. We show that for a large class of linearisable systems this is not the case. In the discrete domain, we investigate whether the singularity confinement property is satisfied for the discrete analogues of the non-Painlevé… (More)

In a recent publication we proposed an extension of Hirota's bilinear formalism to arbitrary multilinearities. The trilinear (and higher) operators were constructed from the requirement of gauge invariance for the nonlinear equation. Here we concentrate on the trilinear case, and use singularity analysis in order to single out equations that are likely to… (More)

While many integrable spin systems are known to exist in (1+1) and (2+1) dimensions , the integrability property of the physically important (2+1) dimensional isotropic Heisenberg ferromagnetic spin system in the continuum limit has not been investigated in the literature. In this paper, we show through a careful singularity structure analysis of the… (More)

- T Takenawa, M Eguchi, B Grammaticos, Y Ohta, A Ramani, J Satsuma
- 2008

We apply the algebraic-geometric techniques developed for the study of mappings which have the singularity confinement property to mappings which are integrable through linearisation. The main difference with respect to the previous studies is that the linearisable mappings have generically unconfined singularities. Despite this fact we are able to provide… (More)