Hirota方程的怪波解及其传输特性研究

求出了高阶Hirota方程在可积条件下的一种精确呼吸子解,并基于此呼吸子解得到了Hirota方程的一种怪波解.在此怪波解的基础上研究了怪波的激发,发现对平面波进行周期性扰动可以激发怪波,对平面波进行高斯扰动可以更快地激发怪波,还可以直接在常数项上增加高斯扰动激发怪波.作为一个实例,采用分步傅里叶方法数值研究了在考虑自频移和拉曼增益时怪波的传输特性,自频移使怪波中心发生偏移,拉曼增益使得怪波分裂得更快,而且拉曼增益值越大怪波分裂得越快,但是拉曼增益对怪波的峰值强度没有明显影响.最后数值模拟了相邻怪波之间的相互作用特点,随着怪波之间距离的减小,怪波将合二为一,成为一束怪波,之后再分裂,并分析了拉曼增益和自频移对怪波相互作用的影响.

Rogue solution of Hirota equation and its transmision

A breather soliton solution of the higher-order Hirota equation is given under the integrable condition, and the rogue solution of Hirota equation is obtained on the basis of the breather soliton solutions, which is helpful to understand the characteristics and the physical reason of rogue wave. The excitation of rogue wave is studied by a cw and periodic perturbation or a Gaussian type perturbation. As an example, by distribution Fourier method, the transmission characteristics of rogue wave is studied with considering the frequency shift and the Raman gain, and the effects of the frequency shift and Raman gain on the interaction between rogue waves are also analyzed.
Keywords：Hirota equationrogue waveRaman gaininteraction