Rogue waves of the Hirota and the Maxwell-Bloch equations.
Rogue waves of the Hirota and the Maxwell-Bloch equations.
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DOI：
10.1103/physreve.87.012913
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发表时间：
2012-05
期刊：
影响因子：
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通讯作者：
Chuanzhong Li;Jingsong He;K. Porsezian
中科院分区：
文献类型：
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作者：
Chuanzhong Li;Jingsong He;K. Porsezian
本文导出了飞秒脉冲在掺铒光纤中传输时所支配的Hirota和Maxwell-Bloch（H-MB）系统的Darboux变换，并将其推广到该系统的n重Darboux变换的矩阵形式。这个n重达布变换意味着从（E，p，η）的已知解生成（E（[n]），p（[n]），η（[n]））的n个解的行列式表示。（E（[n]），p（[n]），η（[n]））的行列式表示提供了H-MB系统的孤子解、位置子解和呼吸子解（亮呼吸子和暗呼吸子）。从呼吸子解出发，我们还构造了H-MB系统的亮暗流氓波解，这是目前数学和物理学中最热门的课题之一。令人惊讶的是，由于p和η的分子和分母的阶数，流氓波解具有两个峰值。同时，在固定时间和空间参数，改变另外两个未知参数α和β后，生成一个异常波形。
In this paper, we derive a Darboux transformation of the Hirota and the Maxwell-Bloch (H-MB) system which is governed by femtosecond pulse propagation through an erbium doped fiber and further generalize it to the matrix form of the n-fold Darboux transformation of this system. This n-fold Darboux transformation implies the determinant representation of nth solutions of (E([n]),p([n]),η([n])) generated from the known solution of (E,p,η). The determinant representation of (E([n]),p([n]),η([n])) provides soliton solutions, positon solutions, and breather solutions (both bright and dark breathers) of the H-MB system. From the breather solutions, we also construct a bright and dark rogue wave solution for the H-MB system, which is currently one of the hottest topics in mathematics and physics. Surprisingly, the rogue wave solution for p and η has two peaks because of the order of the numerator and denominator of them. Meanwhile, after fixing the time and spatial parameters and changing two other unknown parameters α and β, we generate a rogue wave shape.