## Abstract

Abstract: A waveguide occupies a domain G with several cylindrical ends. The waveguide is described by a nonstationary equation of the form iმ_{t}, where A is a selfadjoint second order elliptic operator with variable coefficients (in particular, for A=-Δ, where Δ stands for the Laplace operator, the equation coincides with the Schrödinger equation). For the corresponding stationary problem with spectral parameter, we define continuous spectrum eigenfunctions and a scattering matrix. The limiting absorption principle provides expansion in the continuous spectrum eigenfunctions. We also calculate wave operators and prove their completeness. Then we define a scattering operator and describe its connections with the scattering matrix.

Original language | English |
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Pages (from-to) | 430-433 |

Number of pages | 4 |

Journal | Doklady Physics |

Volume | 64 |

Issue number | 11 |

DOIs | |

State | Published - 1 Nov 2019 |

## Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)