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Abstract <p>We consider singularities of the wavefront of a smooth plane curve in terms of planar vector fields and their singularities. This approach allows to give a complete description of wavefronts, caustics, and their singularities in both generic and degenerate cases. Asymptotic behavior in the neighborhood of singular points of wavefronts and caustics is calculated explicitly. Bifurcations of wavefronts and caustics under curve deformation are considered.</p>

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Wavefronts and Caustics of Vector Fields

  • 期刊论文

  • 发表日期：

    2026年4月1日

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  • V. P. Varin

摘要

Abstract

We consider singularities of the wavefront of a smooth plane curve in terms of planar vector fields and their singularities. This approach allows to give a complete description of wavefronts, caustics, and their singularities in both generic and degenerate cases. Asymptotic behavior in the neighborhood of singular points of wavefronts and caustics is calculated explicitly. Bifurcations of wavefronts and caustics under curve deformation are considered.