2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219269It is shown that third-order 1D nonlinear dispersion equations admit single point gradient catastrophe, described by blow-up-type similarity solutions. After blow-up, the solutions admit shock wave-type self-similar extensions. Snce such extensions are not unique, this implies the principle nonuniqueness of shock-type solutions and also nonexistence of any entropy-type description of proper unique solutions. A difficult free-boundary setting, with extra conditions specified on shocks, are necessary to restore uniqueness in such problems.19 pages, 8 figuresAnalysis of PDEs35K55, 35K40, 35K65text