Darboux transformations on Sturm-Liouville Eigenvalue Problems with Eigenparameter Dependent Transmission Conditions
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg. In fulfillment of the requirements for the degree of Master of Science, 2017 === Sturm-Liouville eigenvalue problems arise prominently in mathematical physics. An innumerous amount of complexities ha...
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| Format: | Others |
| Language: | en |
| Published: |
2018
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| Online Access: | https://hdl.handle.net/10539/24838 |
| Summary: | A dissertation submitted to the Faculty of Science, University of the
Witwatersrand, Johannesburg. In fulfillment of the requirements for the degree
of Master of Science, 2017 === 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. === XL2018 |
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