Refined wave breaking for the generalized Fornberg-Whitham equation
Analysis of PDEs
2026-02-27 v1
Abstract
This paper considers a class of non-local equations that are weakly dispersive perturbations of the inviscid Burgers equation, which includes the Fornberg-Whitham equation as a special case. We precise the known results on finite time blow-up (shock formation) by constructing a blowup solution which displays a `shock-like' singularity (called wave breaking) at one single point. Moreover, this solution converges asymptotically in the self-similar variables to a stable self-similar solution of the inviscid Burgers equation, and also possesses a H\"{o}lder regularity at the blowup point.
Keywords
Cite
@article{arxiv.2602.22924,
title = {Refined wave breaking for the generalized Fornberg-Whitham equation},
author = {Jean-Claude Saut and Yuexun Wang},
journal= {arXiv preprint arXiv:2602.22924},
year = {2026}
}