Near-corner waves of the Camassa-Holm equation

The travelling waves of the Camassa-Holm equation exist only up to a maximum amplitude. The limiting wave has a discontinuous slope, a so-called “corner wave”. Here, we investigate the transition from smooth wave to corner wave through a mixture of matched asymptotic expansions, perturbation theory and numerical computations. There are both striking similarities and equally dramatic differences from other known examples of near-corner waves.