Persistence properties for a generalized Camassa–Holm equation in weighted LpLp 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 LpLp spaces Lpϕ=Lp(R,ϕpdx). Our results extends the work of Brandolese (2012) [2] on persistence properties to more general equation with higher-order nonlinearities.