Generalized Baecklund-Darboux transformation: conservation laws, rational extensions and bispectrality
Alexander Sakhnovich
TL;DR
This paper explores the generalized Baecklund-Darboux transformation (GBDT), focusing on conservation laws, rational extensions, and bispectrality, using nonlinear optics equations as a key example to advance understanding of integrability and symmetry.
Contribution
It introduces a comprehensive analysis of GBDT, highlighting new insights into conservation laws, rational extensions, and bispectrality within integrable systems.
Findings
Identification of conservation laws in GBDT
Construction of rational extensions for nonlinear equations
Demonstration of bispectrality in the context of GBDT
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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