A combined method for computing the field of the point source in a waveguide. (A weakly curved layered medium).

*(Russian, English)*Zbl 1086.35107
J. Math. Sci., New York 132, No. 1, 130-135 (2006); translation from Zap. Nauchn. Semin. POMI 308, 225-234, 256 (2004).

Summary: The two-dimensional problem of propagation of waves, raised by a point source, in an slightly curved waveguide is investigated. The Dirichlet condition is given at the boundary of the wave guide and also two junction condition are defined on the interface between fluid and bottom. The velocity is supposed to be arbitrarily depending with respect to the depth of the waveguide and to be weakly depending with respect to trace coordinate. With the help of an involved transformation the solution is represented as a sum of geometro-optical waves and normal waves. Estimates of the general amount of the detached normal and geometro-optical waves are obtained.

##### MSC:

35Q60 | PDEs in connection with optics and electromagnetic theory |

76Q05 | Hydro- and aero-acoustics |

35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |

78A05 | Geometric optics |

78A50 | Antennas, waveguides in optics and electromagnetic theory |

##### References:

[1] | V. B. Philippov, ”A method for calculating the field of a point source in a waveguide,” Zap. Nauchn. Semin. LOMI, 99, 146–156 (1980). |

[2] | V. B. Philippov, N. Ya. Kirpichnikova, and N. G. Vlasyuk, ”A combined method for calculating the field of a point source in a waveguide (plane-layered media),” Zap. Nauchn. Semin. POMI, 308, 197–224 (2004). · Zbl 1130.35122 |

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