Exceptional circles of radial potentials

M. Music, P. Perry, S. Siltanen

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


A nonlinear scattering transform is studied for the two-dimensional Schrödinger equation at zero energy with a radial potential. Explicit examples are presented, both theoretically and computationally, of potentials with nontrivial singularities in the scattering transform. The singularities arise from non-uniqueness of the complex geometric optics solutions that define the scattering transform. The values of the complex spectral parameter at which the singularities appear are called exceptional points. The singularity formation is closely related to the fact that potentials of conductivity type are 'critical' in the sense of Murata.

Original languageEnglish
Article number045004
JournalInverse Problems
Issue number4
StatePublished - Apr 2013

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics


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