Matrix Hermite-Padé problem and dynamical systems
Consider the system \[ \begin{aligned} b_{n+3} &= b_{n+3}(U_{n+ 3}- U_{n- 2}),\\ U_{n+3} &= b_{n+ 6}(b_{n+ 9}+ b_{n+ 7}+ b_{n+ 5})+ b_{n+ 4}(b_{n+ 7}+ b_{n+ 5})+ b_{n+ 2} b_{n+5}\end{aligned} \] with \(b_{n+3}\equiv 0\), \(n< 0\). The authors consider the Cauchy problem with initial conditions \(b_{n+3}(0)\), \(n\geq 0\). Such systems arise from discrete generalizations of the KdV equation. A representation formula for the solution is given in terms of a matrix continued fraction and a spectral measure. The authors then study the associated Padé-Hermité problem and the differential equation satisfied by the moments of the spectral measure.
scientific article; zbMATH DE number 1548086
scientific article