Persistence properties for a generalized Camassa–Holm equation in weighted spaces

In present paper, we study the Cauchy problem for a generalized Camassa–Holm equation, which was discovered by Hakkaev and Kirchev (2005) [12]. Our purpose here is to establish persistence properties and some unique continuation properties of the solutions of this equation in weighted L p spaces L p ϕ = L p ( R , ϕ p d x ) . Our results extends the work of Brandolese (2012) [2] on persistence properties to more general equation with higher-order nonlinearities.