This study is carried out on the basis on the fourth-order integrable equation(LPD equation) of the Schr dinger hierarchy, which contains both fourth-order dispersion terms and fourth-order nonlinear terms. Firstly, using the Darboux transformation method, we drive a one-breather solution of LPD equation, and the dynamic characteristics of the breather are researched. The conversion relations from breather to W-shaped soliton, oscillation W-shaped soliton and periodic wave are obtained. Secondly, with the aid of the recurrence of the Darboux transformation, the two-breather solutions of the LPD equation are obtained, and the collision characteristics between the breather and the soliton, the breather and the periodic wave are studied by using the transition from the breather to the soliton. Finally, the collision characteristics of two-breather are studied in more details, and the conclusion that the dynamic characteristics of two-breather such as cross-collision, parallel superposition and degenerate state of two-breather are obtained.