Reflectionless Sturm-Liouville equations

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4 Scopus citations


We consider compactly supported perturbations of periodic Sturm-Liouville equations. In this context, one can use the Floquet solutions of the periodic background to define scattering coefficients. We prove that if the reflection coefficient is identically zero, then the operators corresponding to the periodic and perturbed equations, respectively, are unitarily equivalent. In some appendices, we also provide the proofs of several basic estimates, e.g., bounds and asymptotics for the relevant m-functions.

Original languageEnglish (US)
Pages (from-to)207-225
Number of pages19
JournalJournal of Computational and Applied Mathematics
Issue number1 SPEC. ISS.
StatePublished - Nov 1 2007


  • Scattering coefficients
  • Sturm-Liouville equations

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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