Completely integrable nonlinear dynamical systems of the Langmuir chains type (Q1277558)

The paper is devoted to the integration of Langmuir chains. In particular, the main result of it is the following: The chain \[ \ddot{c}_n=c_n(c_{n+2}c_{n+1}-c_{n-1}c_{n-2}) \] such that \(c_{-2}=c_{-1}=0\) and with the sequence \(\{c_n\}_n\) bounded in the positive real numbers has a unique solution. This solution can be recovered by using continuous Markov fractions. Among others, the author uses Hermite-Padé approximations and discrete Sturm-Liouville theory.