In this paper, we study the orbital stability of solitary waves of compound KdV-type equation in the form of ut ＋ auPux ＋ bu2pux ＋ Uzzz = 0 （b 〉 0, p 〉 0）. Our results imply that orbital stability of solitary w...In this paper, we study the orbital stability of solitary waves of compound KdV-type equation in the form of ut ＋ auPux ＋ bu2pux ＋ Uzzz = 0 （b 〉 0, p 〉 0）. Our results imply that orbital stability of solitary waves is affected not only by the highest-order nonlinear term bu2pux, but also the nonlinear term auPux. For the case of b 〉 0 and 0 〈 p ≤ 2, we obtain that the positive solitary wave Ul（X - ct） is stable when a 〉 0, while that unstable when a 〈 0. The stability for negative solitary wave u2（x - ct） is on the contrary. In particular, we point that the nonlinear term with coefficient a makes contributes to the stability of the solitary waves when p= 2 and a〉0.展开更多
基金Supported by the National Natural Science Foundation of China(No.11471215)Innovation Program of Shanghai Municipal Education Commission(No.13ZZ118)+1 种基金Shanghai Leading Academic Discipline Project(No.XTKX2012)Hujiang Foundation of China(No.B14005)
文摘In this paper, we study the orbital stability of solitary waves of compound KdV-type equation in the form of ut ＋ auPux ＋ bu2pux ＋ Uzzz = 0 （b 〉 0, p 〉 0）. Our results imply that orbital stability of solitary waves is affected not only by the highest-order nonlinear term bu2pux, but also the nonlinear term auPux. For the case of b 〉 0 and 0 〈 p ≤ 2, we obtain that the positive solitary wave Ul（X - ct） is stable when a 〉 0, while that unstable when a 〈 0. The stability for negative solitary wave u2（x - ct） is on the contrary. In particular, we point that the nonlinear term with coefficient a makes contributes to the stability of the solitary waves when p= 2 and a〉0.
