非线性薛定谔方程的呼吸子解及其怪波极限

Breather Solutions and Their Rouge Wave Limits of Nonlinear Schr?dinger Equation

采用达布变换法得到了标准非线性薛定谔方程的一阶呼吸子解及其怪波极限,研究了一阶呼吸子解的动力学特性。借助达布变换的递推关系得到了非线性薛定谔方程的高阶呼吸子解,并分别研究了碰撞叠加、分离、简并和并行传输模式。当各呼吸子的频率趋于零时,得到非线性薛定谔方程怪波极限。研究结果表明,怪波幅值、凸起数以及怪波分裂后中心波峰的阶数和周围的波峰个数均与怪波阶数有关。

Based on the standard nonlinear Schr?dinger equation, the first-order breather solution and its rouge wave limit are obtained with Darboux transform method, and the dynamic characteristics of first-order breather solution are studied. High-order breather solutions of nonlinear Schrdinger equation are obtained by means of recurrence relation of Darboux transformation. And their collision superposition, separation, degeneracy and parallel transmission modes are studied, respectively. Nonlinear Schr?dinger equation′s rouge wave limit can be obtained when each breather frequency tends to zero. Research results show that the rouge wave′s amplitude, number of bumps, order of center peaks and number of surrounding peaks after splitting are related to rouge wave′s order.