Abstract: The long time behavior of solutions is one of important problems in the study of partial differential equations. To a great degree, the properties of solutions will depend on those of initial values. The persistence properties imply that the solutions of the equations decay at infinity when the initial data satisfies the condition of decaying at infinity. In this paper, we consider the persistence properties of solutions to the initial value problem for a new generalized two-component Camassa-Holm-type system by using weight functions. Furthermore, we give an optimal decaying estimate.

Key words: generalized Camassa-Holm-type system, optimal decaying estimate, persistence properties