It is pointed out that the higher-order symmetries of the Camassa-Holm (CH) equation are nonlocal and nonlocality poses problems to obtain higher-order conserved densities for this integrable equation (J. Phys. A: Math. Gen. 2005, 38 869-880). This difficulty is circumvented by defining a nolinear hierarchy for the CH equation and an explicit expression is constructed for the nth-order conserve...

Abstract In this article, a numerical solution for the Rosenau-Kawahara equation is considered. A new conservative approximation scheme presented to solve initial boundary value problem of equation, which preserves original properties. The proposed based on finite difference method. existence solutions has been shown by Browder fixed point theorem. priori bound and error estimates, as well cons...

In this paper, we consider the solution map of Cauchy problem to Fokas–Olver–Rosenau–Qiao equation on real line and prove that is not uniformly continuous initial data in Besov spaces. Our result extends previous results Himonas Mantzavinos (Nonlinear Anal 95:499–529, 2014) Li et al. (J Math Fluid Mech 22:50, 2020).