Abstract and Applied Analysis
Volume 2004 (2004), Issue 6, Pages 511-524
doi:10.1155/S108533750430309X

Darboux-Lamé equation and isomonodromic deformation

Abstract

The Darboux-Lamé equation is defined as the double Darboux transformation of the Lamé equation, and is studied from the viewpoint of the isomonodromic deformation theory. It is shown that the second-order ordinary differential equation of Fuchsian type on P1 correspondingto the second Darboux-Lamé equation is obtained as isomonodromic deformation of some specific Gauss' hypergeometric differential equation.