The n-th stationary KdV equation and the monodromy

Abstract

A new scheme for investigating the analytical properties of the solution of the n-th stationary KdV equation is observed with the aid of its algebraic first integrals in involution. For instance, the double periodicity of the solution of the n-th stationary KdV equation is clarified by calculating the monodromy of the differential equation with the regular singular points which are derived from the eigenvalue problem associated with the linearizing operator of the n-th stationary KdV equation. The role of the spectral parameter for the resulting Fuchsian equation is also observed.