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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.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.
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Keywords:
- Hirota equation /
- rogue wave /
- Raman gain /
- interaction
[1] Guo B L 2011 Advances in Math. 40 393 (in Chinese) [郭柏灵 2011 数学进展 40 393]
[2] Taki M, Mussot A, Kudlinski A, Louvergneaux E, Kolobov M, Douay M 2010 Phys. Lett. A 374 691
[3] Tao Y S, He J S, Porsezian K 2013 Chin. Phys. B 22 074210
[4] Ma Z Y, Ma S H 2012 Chin. Phys. B 21 030507
[5] Zhang J F, Jin M Z, He J D 2013 Chin. Phys. B 22 054208
[6] Yang G Y, Li L, Jia S T 2012 Phys. Rev. E 85 046608
[7] Sakovich S Y 1997 J. Phys. Soc. Japan 66 2527
[8] Karpman V I 2004 Eur. Phys. J. B 39 341
[9] Li S Q, Li L, Li Z H 2004 J. Opt. Soc. Am. B 21 2089
[10] Ablowitz M J, Clarkson P A 1991 Soliton Nonlinear Evolution Equations and Inverse Scattering (England: Cambridge University Press) pp34-68
[11] Zhang J F, Hu W C 2013 Chin. Opt. Lett. 11 031901
[12] Qiao H L, Jia W G, Liu B L, Wang X D, Menke N M L, Yang J, Zhang J P 2013 Acta Phys. Sin. 62 104212 (in Chinese) [乔海龙, 贾维国, 刘宝林, 王旭东, 门克内木乐, 杨军, 张俊萍 2013 物理学报 62 104212]
[13] Li S Q, Li L, Li Z H 2004 Acta Photon. Sin. 33 826 (in Chinese) [李淑青, 李录, 李仲豪 2004 光子学报 33 826]
[14] Zhang J F 2013 Acta Opt. Sin. 33 0419001 (in Chinese) [张解放 2013 光学学报 33 0419001]
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[1] Guo B L 2011 Advances in Math. 40 393 (in Chinese) [郭柏灵 2011 数学进展 40 393]
[2] Taki M, Mussot A, Kudlinski A, Louvergneaux E, Kolobov M, Douay M 2010 Phys. Lett. A 374 691
[3] Tao Y S, He J S, Porsezian K 2013 Chin. Phys. B 22 074210
[4] Ma Z Y, Ma S H 2012 Chin. Phys. B 21 030507
[5] Zhang J F, Jin M Z, He J D 2013 Chin. Phys. B 22 054208
[6] Yang G Y, Li L, Jia S T 2012 Phys. Rev. E 85 046608
[7] Sakovich S Y 1997 J. Phys. Soc. Japan 66 2527
[8] Karpman V I 2004 Eur. Phys. J. B 39 341
[9] Li S Q, Li L, Li Z H 2004 J. Opt. Soc. Am. B 21 2089
[10] Ablowitz M J, Clarkson P A 1991 Soliton Nonlinear Evolution Equations and Inverse Scattering (England: Cambridge University Press) pp34-68
[11] Zhang J F, Hu W C 2013 Chin. Opt. Lett. 11 031901
[12] Qiao H L, Jia W G, Liu B L, Wang X D, Menke N M L, Yang J, Zhang J P 2013 Acta Phys. Sin. 62 104212 (in Chinese) [乔海龙, 贾维国, 刘宝林, 王旭东, 门克内木乐, 杨军, 张俊萍 2013 物理学报 62 104212]
[13] Li S Q, Li L, Li Z H 2004 Acta Photon. Sin. 33 826 (in Chinese) [李淑青, 李录, 李仲豪 2004 光子学报 33 826]
[14] Zhang J F 2013 Acta Opt. Sin. 33 0419001 (in Chinese) [张解放 2013 光学学报 33 0419001]
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