Possibility of an Akhmediev breather decaying into solitons
Possibility of an Akhmediev breather decaying into solitons
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DOI：
10.1103/physreva.85.033808
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发表时间：
2012-03
影响因子：
2.9
通讯作者：
C. Mahnke;F. Mitschke
中科院分区：
文献类型：
--
作者：
C. Mahnke;F. Mitschke
考虑了非线性薛定谔方程的常数解或宽脉冲解通过调制不稳定性转化为孤子系综的过程.这一过程通常被认为是在光纤中产生超连续谱的一个重要步骤。从Akhmediev呼吸子解出发，我们研究了两种方法的转换：一种是面向脉冲形状，利用孤子宽度和峰值功率之间的关系。另一种是面向特征值的，使用散射理论的结果。很明显，根据未修正的非线性薛定谔方程的演化，即使在噪声存在下，也不会导致孤子的转化。然而，如果考虑到拉曼效应，则发生向孤子气体的转化。
We consider the process by which a constant or wide-pulse solution of the nonlinear Schr\"odinger equation can become converted into an ensemble of solitons by modulational instability. This process is generally believed to be one important step in the generation of supercontinuum in optical fibers. Starting from the Akhmediev breather solution we study the conversion by two methods: One is pulse shape-oriented and uses the soliton relation between width and peak power. The other is eigenvalue-oriented and uses results from scattering theory. It becomes clear that an evolution according to the unmodified nonlinear Schr\"odinger equation, even in the presence of noise, will not lead to the transformation into solitons. If one takes the Raman effect into account, however, a conversion to a soliton gas takes place.