A Liouville theorem for the Degasperis-Procesi equation
arXiv:1405.6675
Abstract
We prove that the only global, strong, spatially periodic solution to the Degasperis-Procesi equation, vanishing at some point (t0, x0), is the identically zero solution. We also establish the analogue of such Liouville-type theorem for the Degasperis-Procesi equation with an additional dispersive term.
Post-refereeing version. To appear on Annali Scienze Scuola Norm. Sup. Pisa. Doi 10.2422/2036-2145.201410\_014