负五阶非线性下高阶孤子分裂的数值模拟

从光纤中包含五阶非线性的扩展非线性薛定谔方程组出发，采用分步傅立叶算法，以五到八阶孤子为例，数值模拟了负五阶非线性对高阶孤子波形演化的影响。研究表明，负五阶非线性下高阶孤子的演化不再有周期性，而是分裂成一对较强的主脉冲和一定数量的弱脉冲，且相对于中心对称的主脉冲对和弱脉冲对都可能因相互排斥而随距离的增加相互远离，分裂成的脉冲数目及相互远离的速度将随负五阶非线性参数及孤子本身的阶数而不同。对于阶数相对低的五、六阶孤子，在较弱的负五阶非线性时，靠近中心的弱脉冲对将出现周期性的排斥和吸引现象。相比较而言，阶数高的七、八阶孤子分裂出的脉冲数一般更多，脉冲对因相互排斥而互相远离的速度也更快。

Numerical simulation of splitting of high-order solitons in case of negative quintic nonlienaity

Starting from the extended nonlinear Schrodinger equations including quintic nonlinearity in optical fibers, adopting the split- step Fourier algorithm, taking the fifth - to eighth - order solitons for example, the effect of the negative quintic nonlinearity on the shape evolution of the high - order solitons was numerically simulated. The results show that, the high - order solitons will lose their periodicity and split into a pair of intense pulse and some weak pulses during propagation in case of negative quintic nonlinearity. Moreover, the main pulse pair and other weak pulse pairs which are central symmetric may repulse and depart from each other with the propagation distance. Depending on different parameters of negative quintie nonlinearity and different orders of solitons, the number of splitted pulses and the velocity of the pulse pairs depart from each other may also be different. For the fifth - and sixth - order soliton whose soliton order number is relatively low, when the parameters of negative quintic nonlinearity are small,the weak pulse pair which is close to the center will repulse and attract periodically. In comparison, for the seventh - and eighth - order seliton whose soliton order number is high, more pulses will be splitted generally. Furthermore, the velocity of the pulse pairs repulse and depart from each other will be faster.