Breathers and breather-rogue waves on a periodic background for the derivative nonlinear Schrödinger equation
Breathers and breather-rogue waves on a periodic background for the derivative nonlinear Schrödinger equation
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DOI：
10.1088/1402-4896/ab783e
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发表时间：
2020-03
期刊：
影响因子：
2.9
通讯作者：
Bo Xue;Jing Shen;X. Geng
中科院分区：
文献类型：
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作者：
Bo Xue;Jing Shen;X. Geng
本文给出了周期背景下导数非线性薛定谔方程的行列式形式的解。由于其在周期背景下的流氓波已经被研究过了，我们只研究了导数非线性薛定谔方程在周期背景下的呼吸子和呼吸子-流氓波。我们得到了该方程在周期背景下的Kuznetsov-Ma呼吸子、Akhmediev呼吸子和时空呼吸子。此外，我们还研究了周期背景下三种类型的呼吸子-流氓波：（1）一个孤立子与一个呼吸子的相互作用;（2）一个孤立子与两个呼吸子的相互作用;（3）一个二阶流氓波与一个呼吸子的相互作用。对于第一类，我们分析了自由参数对其动力学行为的影响。第二种类型被描述为周期性背景上的“流氓波量子”。第三类具有基本型和三角型两种时空分布结构。
In this paper, we give the solutions on a periodic background in terms of the determinant form for the derivative nonlinear Schrödinger equation. Because its rogue wave on a periodic background has been studied, we investigate only the breather and breather-rogue wave on a periodic background for the derivative nonlinear Schrödinger equation. We obtain Kuznetsov–Ma breather, Akhmediev breather and spatio-temporal breather on a periodic background for this equation. In addition, we mainly focus on three types of the breather-rogue wave on a periodic background: (1) the interaction between a Peregrine soliton and a breather; (2) the interaction between a Peregrine soliton and two breathers; (3) the interaction between a second-order rogue wave and a breather. For the first type, we analyse the effects of the free parameters on its dynamical behaviour. The second type is described as ‘rogue wave quanta’ on a periodic background. The third type has two spatial-temporal distribution structures: the fundamental structure and the triangular structure.