Abstract and Applied Analysis
Volume 2004 (2004), Issue 6, Pages 511-524

Darboux-Lamé equation and isomonodromic deformation

Mayumi Ohmiya

School of Engineering, Doshisha University, Kyotanabe 610-0394, Japan

Received 10 September 2002

Copyright © 2004 Mayumi Ohmiya. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.