On the Riccati equations for the scattering matrices in two dimensions

Y. Chen, V. Rokhlin

Research output: Contribution to journalArticlepeer-review


We introduce the scattering matrices for the two-dimensional scattering problem for the Helmholtz equation. Naturally connected with the far-field scattering amplitude, the scattering matrices provide a forward model which governs the behaviour of the scattering process at any given frequency, and which is in turn described by a system of ordinary differential equations. The latter can be solved numerically in a stable manner and with arbitrary precision. The scattering matrices possess a rich analytical structure, which makes them an effective tool for the inverse scattering both analytically and numerically.

Original languageEnglish (US)
Pages (from-to)1-13
Number of pages13
JournalInverse Problems
Issue number1
StatePublished - 1997

ASJC Scopus subject areas

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


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