Schlesinger Transformations for Linearisable Equations

Details Schlesinger Transformations for Linearisable Equations Schlesinger Transformations for Linearisable Equations

1998-07-07

arxiv.org/abs/solv-int/9807003v1

Lett.Math.Phys. 46, 131-145 (1998).

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, no figures, Tex file

Scientific paper

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 of steps for singularity confinement. Two Schlesinger transformations are obtained relating the solutions for some value $n$ to that corresponding to either n+1 or n+2.

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