Abstract
Wave fields excited by moving oscillating sources are considered. In the resonance case, the asymptotics of the far field for large values of t is found. Explicit expressions for the growing components of the field are provided.
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References
J. Lighthill, “Studies on magneto-hydrodynamic waves and other anisotropic wave motions,”Phil. Trans. Roy. Soc. London, Ser. A,252, No. 1014, 397–430 (1960).
J. Lighthill,Waves in Fluids, Cambridge Univ. Press (1978).
L. Chee-Seng, “Water waves generated by an oscillatory surface pressure travelling at critical speed,”Wave Motion,3, 159–180 (1981).
M. Yanovitch, “Gravity waves in a heterogeneous incompressible fluid,”Commun. Pure Appl. Math,15 45–52 (1962).
M. V. Fedoryuk,The Method of Steepest Descent [in Russian], Nauka, Moscow (1977).
V. A. Borovikov,Uniform Stationary-Phase Method, IEE, Electromagnetic Waves Ser., Vol. 40, London (1994).
A. P. Anyutin and V. A. Borovikov,Uniform Asymptotics of Integrals with Quickly Oscillating Integrands and Singularities of the Nonexponential Factor [in Russian], Moscow (1984).
T. Pearcey, “The structure of an electromagnetical field in the neighbourhood of a cusp of a caustic,”Philos. Mag.,37, 311–317 (1946).
D. Ludwig, “Uniform asymptotic expansions at a caustic,”Commun. Pure Appl. Math.,19, No. 2, 215–250 (1966).
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 61–70.
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Borovikov, V.A. The far field excited by a moving oscillating source in the resonance case. J Math Sci 96, 3321–3326 (1999). https://doi.org/10.1007/BF02172807
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DOI: https://doi.org/10.1007/BF02172807