On the Riccati equations for the scattering matrices in two dimensions

Y. Chen, V. Rokhlin

Research output: Contribution to journalArticle

Abstract

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
Volume13
Issue number1
DOIs
StatePublished - 1997

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Riccati equation
Riccati equations
Scattering Matrix
S matrix theory
Riccati Equation
Two Dimensions
Scattering
Helmholtz equations
Scattering Amplitude
Inverse Scattering
inverse scattering
Scattering Problems
Helmholtz Equation
Far Field
scattering
System of Ordinary Differential Equations
scattering amplitude
far fields
differential equations
Arbitrary

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

On the Riccati equations for the scattering matrices in two dimensions. / Chen, Y.; Rokhlin, V.

In: Inverse Problems, Vol. 13, No. 1, 1997, p. 1-13.

Research output: Contribution to journalArticle

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