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Journal of Mathematics
Volume 2013 (2013), Article ID 645752, 10 pages
http://dx.doi.org/10.1155/2013/645752
Research Article

Wronskian Addition Formula and Darboux-Pöschl-Teller Potentials

Institut de Mathématiques de Bourgogne, UMR 5584 CNRS, Université de Bourgogne, Faculté des Sciences Mirande, 9 Avenue Alain Savary, BP 47870, 21078 Dijon Cedex, France

Received 30 November 2012; Accepted 25 February 2013

Academic Editor: Alberto Enciso

Copyright © 2013 Pierre Gaillard and Vladimir Matveev. 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.

Abstract

For the famous Darboux-Pöschl-Teller equation, we present new wronskian representation both for the potential and the related eigenfunctions. The simplest application of this new formula is the explicit description of dynamics of the DPT potentials and the action of the KdV hierarchy. The key point of the proof is some evaluation formulas for special wronskian determinant.