Wavefronts and Caustics of Vector Fields
Abstract
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.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Differential Equations and Numerical Methods
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- Computational Mathematics and Mathematical Physics
- Publisher
- Pleiades Publishing Ltd
- Volume
- 66
- Issue
- 4
- Pages
- 609–622
- Publication date
- 1 April 2026
- Language
- EN