Bäcklund transformations for the rational Lagrange chain

Abstract

We consider a long--range homogeneous chain where the local variables are the generators of the direct sum of $N$ $\mathfrak{e}(3)$ interacting Lagrange tops. We call this classical integrable model rational ``Lagrange chain'' showing how one can obtain it starting from $\mathfrak{su}(2)$ rational Gaudin models. Moreover we construct one- and two--point integrable maps (Bäcklund transformations).

12 pages

References in corpus (2)

• Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top
• Separation of variables and Bäcklund transformations for the symmetric Lagrange top

Cited by in corpus (3)

• Bäcklund Transformations as exact integrable time-discretizations for the trigonometric Gaudin model
• From su(2) Gaudin Models to Integrable Tops
• An integrable discretization of the rational su(2) Gaudin model and related systems