2009/10/19 by J. Eggers M. A. Fontelos, Fontelos, J. Eggers M. A.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.0910.3499
arxiv created 2009/10/19 · arxiv updated 2009/12/01
A wide range of equations related to free surface motion in two dimensions exhibit the formation of cusp singularities either in time, or as function of a parameter. We review a number of specific examples, relating in particular to fluid flow and to wave motion, and show that they exhibit one of two types of singularity: cusp or swallowtail. This results in a universal scaling form of the singularity, and permits a tentative classification.