### 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 language | English (US) |
---|---|

Pages (from-to) | 1-13 |

Number of pages | 13 |

Journal | Inverse Problems |

Volume | 13 |

Issue number | 1 |

DOIs | |

State | Published - 1997 |

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### ASJC Scopus subject areas

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

### Cite this

*Inverse Problems*,

*13*(1), 1-13. https://doi.org/10.1088/0266-5611/13/1/001

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

Research output: Contribution to journal › Article

*Inverse Problems*, vol. 13, no. 1, pp. 1-13. https://doi.org/10.1088/0266-5611/13/1/001

}

TY - JOUR

T1 - On the Riccati equations for the scattering matrices in two dimensions

AU - Chen, Y.

AU - Rokhlin, V.

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0002422474&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002422474&partnerID=8YFLogxK

U2 - 10.1088/0266-5611/13/1/001

DO - 10.1088/0266-5611/13/1/001

M3 - Article

VL - 13

SP - 1

EP - 13

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 1

ER -