Persistence properties and asymptotic behavior for a two-component [formula omitted]-family system with high order nonlinearity

Abstract

This paper is devoted to the study of persistence properties and asymptotic behavior for a two-component b-family system with high order nonlinearity. We prove that both the density and momentum components of the corresponding solutions with initial compact support will retain the property of being compactly supported throughout its evolution. Moreover, we investigate the asymptotic behaviors of the solutions at infinity within its lifespan when the initial data decay exponentially and algebraically, respectively.