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GBDT of discrete skew-selfadjoint Dirac systems and explicit solutions of the corresponding non-stationary problems

  • Alexander L. SakhnovichEmail author
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 271)

Abstract

Generalized Bäcklund–Darboux transformations (GBDTs) of discrete skew-selfadjoint Dirac systems have been successfully used for explicit solving of the direct and inverse problems of Weyl–Titchmarsh theory. During explicit solving of direct and inverse problems, we considered GBDTs of the trivial initial systems. However, GBDTs of arbitrary discrete skew-selfadjoint Dirac systems are important as well and we introduce these transformations in the present paper. The obtained results are applied to the construction of explicit solutions of the interesting related non-stationary systems.

Keywords

Discrete skew-selfadjoint Dirac system generalized Bäcklund–Darboux transformation fundamental solution non-stationary system explicit solution 

Mathematics Subject Classification (2010)

Primary 34A05 Secondary 39A06 39A12 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität WienOskar-Morgenstern-Platz 1Austria

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