Generalized Baecklund-Darboux transformation: conservation laws, rational extensions and bispectrality

Abstract

Baecklund-Darboux transformations are closely related to the integrability and symmetry problems. For the generalized Baecklund-Darboux transformation (GBDT), we consider conservation laws, rational extensions and bispectrality. We use the case of the nonlinear optics equation (and its auxiliary linear system) as an example.

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• Solvable rational extensions of the isotonic oscillator
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