2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124814In this paper, we solve the Camassa-Holm equation for a relatively large class of initial data by using a factorization problem on the Hilbert-Schmidt group.27 pages. The paper has been thoroughly revised, with new results added and typos corrected. Final version to appear in CPAMAnalysis of PDEsMathematical Physics35C15, 35Q35, 37K99text