In terms of Darboux transformation, we have exactly solved the higher-order nonlinear Schr6dinger equation that describes the propagation of ultrashort optical pulses in optical fibers. We discuss the modulation insta...In terms of Darboux transformation, we have exactly solved the higher-order nonlinear Schr6dinger equation that describes the propagation of ultrashort optical pulses in optical fibers. We discuss the modulation instability （MI） process in detail and find that the higher-order term has no effect on the MI condition. Under different conditions, we obtain Kuznetsov-Ma soliton and Akhmediev breather solutions of higher-order nonlinear Schredinger equation. The former describes the propagation of a bright pulse on a continuous wave background in the presence of higher-order effects and the soliton＇s peak position is shifted owing to the presence of a nonvanishing background, while the latter implies the modulation instability process that can be used in practice to produce a train of ultrashort optical soliton pulses.展开更多
Based on the developed Darboux transformation, we investigate the exact asymmetric solutions of breather and rogue waves in pair-transition-coupled nonlinear Schr?dinger equations. As an example, some types of exact b...Based on the developed Darboux transformation, we investigate the exact asymmetric solutions of breather and rogue waves in pair-transition-coupled nonlinear Schr?dinger equations. As an example, some types of exact breather solutions are given analytically by adjusting the parameters. Moreover, the interesting fundamental problem is to clarify the formation mechanism of asymmetry breather solutions and how the particle number and energy exchange between the background and soliton ultimately form the breather solutions. Our results also show that the formation mechanism from breather to rogue wave arises from the transformation from the periodic total exchange into the temporal local property.展开更多
In this paper, we use the representation of the solutions of the focusing nonlinear Schrodinger equation we have constructed recently, in terms of wronskians;when we perform a special passage to the limit, we get quas...In this paper, we use the representation of the solutions of the focusing nonlinear Schrodinger equation we have constructed recently, in terms of wronskians;when we perform a special passage to the limit, we get quasi-rational solutions expressed as a ratio of two determinants. We have already construct breathers of orders N = 4, 5, 6 in preceding works;we give here the breather of order seven.展开更多
基金supported by the Key Project of Scientific and Technological Research in Hebei Province,China(Grant No.ZD2015133)
文摘In terms of Darboux transformation, we have exactly solved the higher-order nonlinear Schr6dinger equation that describes the propagation of ultrashort optical pulses in optical fibers. We discuss the modulation instability （MI） process in detail and find that the higher-order term has no effect on the MI condition. Under different conditions, we obtain Kuznetsov-Ma soliton and Akhmediev breather solutions of higher-order nonlinear Schredinger equation. The former describes the propagation of a bright pulse on a continuous wave background in the presence of higher-order effects and the soliton＇s peak position is shifted owing to the presence of a nonvanishing background, while the latter implies the modulation instability process that can be used in practice to produce a train of ultrashort optical soliton pulses.
基金Project supported by the National Natural Science Foundation of China(Grant No.61774001)the Natural Science Foundation of Hunan Province,China(Grant No.2017JJ2045)
文摘Based on the developed Darboux transformation, we investigate the exact asymmetric solutions of breather and rogue waves in pair-transition-coupled nonlinear Schr?dinger equations. As an example, some types of exact breather solutions are given analytically by adjusting the parameters. Moreover, the interesting fundamental problem is to clarify the formation mechanism of asymmetry breather solutions and how the particle number and energy exchange between the background and soliton ultimately form the breather solutions. Our results also show that the formation mechanism from breather to rogue wave arises from the transformation from the periodic total exchange into the temporal local property.
文摘In this paper, we use the representation of the solutions of the focusing nonlinear Schrodinger equation we have constructed recently, in terms of wronskians;when we perform a special passage to the limit, we get quasi-rational solutions expressed as a ratio of two determinants. We have already construct breathers of orders N = 4, 5, 6 in preceding works;we give here the breather of order seven.
