Cusps in interfacial problems
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.
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