Local well-posedness and blow-up for a family of $U(1)$-invariant peakon equations

Abstract

The Cauchy problem for a unified family of integrable $U(1)$-invariant peakon equations from the NLS hierarchy is studied. As main results, local well-posedness is proved in Besov spaces, and blow-up is established through use of an $L^1$ conservation law.

arXiv comment29 pages

References in corpus (7)

• An integrable shallow water equation with peaked solitons
• The Camassa-Holm equation as a geodesic flow on the diffeomorphism group
• Long-Time Asymptotics for the Camassa-Holm Equation
• Generalised Fourier transform for the Camassa-Holm hierarchy
• A new two-component integrable system with peakon solutions
• Local well-posedness and blow-up criteria for a two-component Novikov system in the critical Besov space
• The dynamics of conservative peakons in the NLS hierarchy