We consider singularities of the wave front of a smooth plane curve from the viewpoint of planar vector fields and their singularities. This approach allows giving complete description of wave fronts, caustics, and their singularities in generic cases as well as in degenerate ones. We give explicit formulas for asymptotics in the neighborhood of singular points of wave fronts and caustics. We study some bifurcations of wave fronts and caustics under deformations of the curve.
Mathematical problems and theory of numerical methods