变系数Hirota方程中高阶色散对多压缩点Peregrine怪波梳的影响

Effect of High-order Dispersion on Peregrine Rogue Wave Comb with Multiple Compression Points for Variable-coefficients Hirota Equation

本文基于空间周期调制的Hirota方程的精确解,研究了呼吸解的演化特性及Peregrine怪波梳的产生。结果表明,增大二阶色散系数的调制强度,会影响怪波解的空间分布,在传输方向产生多个压缩点,形成梳状结构,并且压缩点的个数随着二阶色散调制强度的增加成对增加。此外,讨论了三阶色散对多压缩点所产生的影响。结果表明,引入特定形式的三阶色散,不会影响Peregrine怪波梳的产生,并且通过调整三阶色散的系数,能够抑制Peregrine怪波梳产生过程中次高峰的出现。

Based on the analytical solutions of Hirota equation with spatially periodic modulation coefficients,we present the evolution characteristics of breather solution and the generation of Peregrine rogue wave comb.The results demonstrate that increasing the modulation intensity of the second-order dispersion coefficient will impact the spatial distribution of the Peregrine soliton solution,and generate multiple compressed points along the transmission direction,forming a comb-like structure.The number of compressed points increases in pairs with the increase of modulation intensity of the second-order dispersion.Moreover,the effect of the third-order dispersion on breath solution with multiple compression points is considered.It is demonstrated that the third-order dispersion will shift the multiple compressed points and the shape of the multiple compressed points varies with the form of the third-order dispersion.Specially,introducing the specific form of the third-order dispersion,it does not affect the generation peregrine rouge wave comb and the appearance of the sub-peak in forming of the peregrine rough wave comb can be suppressed by adjusting the coefficient of the third-dispersion.