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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
##### Keywords:
Helmholtz equation; interference
##### References:
  V. B. Philippov, ”A method for calculating the field of a point source in a waveguide,” Zap. Nauchn. Semin. LOMI, 99, 146–156 (1980).  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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