中文摘要：

为了研究Hirota方程的二阶怪波解和它在光纤中的传输特性,数值分析了二阶怪波的形成机理,并采用分步傅里叶方法数值模拟了二阶怪波在光纤中的传输特点.结果表明：二阶怪波可以看作两个怪波逐渐靠近的结果;在光纤中传输时,随着距离的增加,二阶怪波最终分裂成两组次波,每组次波的能量值降为初值的一半,它们之间的距离越来越大且互不干扰,并随着距离的增加能量逐渐降低.数值分析了自陡峭和自频移对二阶怪波传输的影响,发现自陡峭引起二阶怪波在传播过程中左波峰能量大于右波峰能量,自频移使怪波的中心发生了非线性偏离,且参数的正负决定偏离的方向.

英文摘要：

In order to study the 2-order rogue solution of Hirota equation and its transmision,the formation mehanism of the 2-order rogue was numerical analyzed and the characteristic of the 2-order rogue wave propagation in the fiber was simulated by the fast Fourier transform.It is found that the 2-order rogue wave can be regarded as the two 1-order waves superposition.In the transmission process,the 2-order rogue wave is firstly split into two rogue waves,and the energy of the 2-order wave is reduced by half,and the distance between them is bigger but there is no mutual interference.Finally,the effects of self-steepening and self-frequency shift for 2-order rogue were numerical analyzed.The results show that self-steepening causes the energy of left wave bigger than right wave,and self-frequency shift makes the center of rogue wave nonlinear deviated,and the parameters decide the direction of deviate.