Darboux transformations on Sturm-Liouville eigenvalue problems with eigenparameter dependant transmission conditions
Date
2017
Authors
Phalafala, Rakgwahla, Jessica
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Abstract
Sturm-Liouville eigenvalue problems arise prominently in mathematical physics.
An innumerous amount of complexities have been encountered in solving these
problems and a myriad of techniques have been explored over the century. In
this work, we investigate one such technique, namely the Darboux-Crum trans
formation. This transformation transforms an existing problem into one that is
readily solvable or displays properties that are better understood. In particular,
we focus our attention on the e↵ect the Darboux-Crum transformation has on the
eigenparameter dependence of the transmission condition of our Sturm-Liouville
eigenvalue problem.
Description
A dissertation submitted in fulfillment of the requirements for the degree
of Master of Science to the Faculty of Science, University of the
Witwatersrand, Johannesburg, 2017
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Citation
Phalafala, Rakgwahla Jessica (2018) Darboux transformations on Sturm-Liouville eigenvalue problems with eigenparameter dependant transmission conditions, University of the Witwatersrand, Johannesburg, https://hdl.handle.net/10539/24838