The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations
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We obtain isomonodromic transformations for Heun's equation by generalizing the Darboux transformation, and we find pairs and triplets of Heun's equation which have the same monodromy structure. By composing generalized Darboux transformations, we establish a new construction of the commuting operator which ensures that the finite-gap property is satisfied. As an application, we prove some previous conjectures in part III.
- © 2006, the Authors. Published by Atlantis Press.
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Cite this article
TY - JOUR AU - Kouichi Takemura PY - 2006 DA - 2006/11/01 TI - The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations JO - Journal of Nonlinear Mathematical Physics SP - 584 EP - 611 VL - 13 IS - 4 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2006.13.4.11 DO - 10.2991/jnmp.2006.13.4.11 ID - Takemura2006 ER -