四阶非线性薛定谔方程中呼吸子解的特性研究

Characteristics of Breather Solutions in the Fourth-Order Nonlinear Schrdinger Equation

基于同时包含四阶色散项和四阶非线性项的非线性薛定谔层级结构的四阶可积方程(LPD方程),首先利用达布变换法得到LPD方程的单呼吸子解,并对呼吸子的动力学特性进行研究,得到呼吸子与W型孤子、抖动的W型孤子和周期波的转换关系;其次,借助达布变换的递推关系得到LPD方程的双呼吸子解,并利用呼吸子与孤子之间的转换关系,研究呼吸子与孤子以及呼吸子与周期波的碰撞特性;最后,对双呼吸子的碰撞特性进行更为详细的研究,得到双呼吸子的交叉碰撞、平行叠加及双呼吸子的简并态等动力学特性。

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.