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<p><i>The</i> 3<i>D short wave diffraction by a compact body with smooth strongly convex boundary is considered. A particular interest presents the diffraction wave field in the vicinity of the light-shadow curve on the scatterer surface. This curve is the geometrical locus of tangent points of incident rays. In</i> 2<i>D case, this problem was first studied by V.&#xa0;A.&#xa0;Fock a long time ago and is now called the Fock problem. However, in the</i> 3<i>D case, additional difficulties arise: i) in the shadowed part of the boundary, the diffraction wave field slides along geodesics which may form caustics, ii) the geodesics are not plane curves. A solution to the 3D Fock problem is proposed in terms of a superposition (integral) of asymptotic solutions of the wave equation localized in the vicinity of every geodesics from corresponding geodesic flow. The solution gets over the difficulties with caustics. Bibliography:</i> 6 <i>titles.</i></p>

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ASYMPTOTIC SOLUTIONS TO V. A. FOCK’S PROBLEM IN 3D, LOCALIZED IN A NEIGHBORHOOD OF A GEODESIC

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • M. M. Popov

摘要

The 3D short wave diffraction by a compact body with smooth strongly convex boundary is considered. A particular interest presents the diffraction wave field in the vicinity of the light-shadow curve on the scatterer surface. This curve is the geometrical locus of tangent points of incident rays. In 2D case, this problem was first studied by V. A. Fock a long time ago and is now called the Fock problem. However, in the 3D case, additional difficulties arise: i) in the shadowed part of the boundary, the diffraction wave field slides along geodesics which may form caustics, ii) the geodesics are not plane curves. A solution to the 3D Fock problem is proposed in terms of a superposition (integral) of asymptotic solutions of the wave equation localized in the vicinity of every geodesics from corresponding geodesic flow. The solution gets over the difficulties with caustics. Bibliography: 6 titles.